Document Type : Research Article
Authors
- Sakineh Chavoshi ^{} ^{1}
- Mani Safamirzaei ^{2}
- F Pajoum Shariati ^{2}
^{1} Master Student of Process Engineering, Faculty of Petroleum and Chemical Engineering, Department of Chemical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
^{2} Assistant Professor, Faculty of Petroleum and Chemical Engineering, Department of Chemical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
Abstract
One of the important, practical and simple methods for hydrate formation condition
is empirical equations, and so far many empirical equations have been presented to predict the
temperature and pressure of hydrate formation. In this study, the methods and empirical
correlations have been reviewed and their predictive capabilities have been evaluated with the
use of more than 2000 experimental data collected from literature. These data have been
separated in three groups: (1) simple natural gas components included methane, ethane,
propane, isobutane, carbon dioxide, nitrogen, and hydrogen sulfide (2) binary gas mixtures
and (3) gas mixture similar to natural gas. In this paper, after expressing the restrictions of
some empirical correlations have been proposed by scientists before and proposed empirical
correlation in the present study, the results of evaluating have been presented in several
tables and curves. The proposed empirical correlation in the present study has shown reliable
performance for both simple natural gas components and mixtures. Despite the existence
three adjustable parameters, the accuracy of this equation shows the ranking 1 to 3 compare
to the rest of the equations.
Keywords
- Empirical Correlations
- Gas Hydrate Formation Condition
- Natural Gas Mixtures
- Hydrate Formation Predicting
- Hydrate Formation Temperature
Main Subjects
Introduction
Natural gas (NG) is a gas consisting primarily
of methane, which forms naturally in the
underground floors (Sahabi, 1996). Raw
natural gas comes from three types of wells: oil
wells, gas wells, and condensate wells.
Whatever the source of the natural gas, once
separated from crude oil (if present), it
commonly exists in mixtures with other
hydrocarbons, principally ethane, propane,
butane, and pentanes. Associated
hydrocarbons, known as “natural gas liquids”
(NGL), are used as raw materials for oil
refineries or petrochemical plants and as
sources of energy (Devold, 2013). These liquids
present about 0.07 per thousand of natural gas
(Sahabi, 1996).
In addition to natural gas liquids, there are
other impurities in natural gas, such as N2,
CO2, water vapor, H2S. Water vapor is the
most common undesirable impurity found in
natural gas. By virtue of its source, natural gas
is almost always associated with water usually
in the range of 400-500 lb water vapor/MMscf
gas (Kumar, 1987).
Liquid water with natural gas lead to some
problems which one of the most important is
gas hydrate formation. Gas hydrates, which
are ice-like structures of water and gas
considered as the unconventional gas sources
(Mokhatab, Poe, & Speight, 2006). Gas
hydrates may lead to several industrial
problems, such as erosion and/or corrosion in
pipelines, the blockage of transfer lines,
compressor damage, etc., which cost millions of
dollars in production facilities and
transmission pipelines every year (Safamirzaei
& Modarress, 2011). On the other hand, due to
the presence of large amounts of hydrocarbons,
16 Gas Processing Journal, Vol. 6, No. 1, 2018
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the formation of hydrates can lead to fire in
the equipment. For example, the explosion and
fire incident occurred in the refrigeration
towers of Bandar Iamam Petrochemical
Company in 3122, which was due to the
formation of propane gas hydrate in the
absorbent beds of the tower (Kazempour,
2011).
Clathrate hydrates have been a source of
problems in the energy industry because the
conditions at which oil and gas are produced,
transported, and processed are frequently
suitable for clathrate hydrate formation
(Englezos, 1993). In order to prevent the
formation of hydrate; gas stream is dehydrated
in different stages of refining and transfer.
Since 1934, the time of discovery of
hydrates in pipelines by Hummer schmidt
(Hammerschmidt, 1934), many investigations
have been done about natural gas hydrates
and avoiding hydrate formation and several
correlations have been presented to facilitate
hydrate formation prediction and
interpretation.
In this study, the methods and empirical
correlations for predicting gas hydrate
formation temperature have been reviewed
and their applications have been evaluated.
The empirical correlations include Motiee
(Motiee, 1991), Tolwer and Mokhatab (Towler
& Mokhatab, 2005), Hammer schmidt
(Hammerschmidt, 1934), Safamirzaei
(Safamirzaei M. , 2015), Bahadori (Bahadori,
2009) , Berge (Berge, 1986) and proposed
empirical correlation in the present study. The
results of evaluating have been presented in
several tables and curves and finally it has
been determined that which empirical
correlation spresent the perfect results for each
group of compounds.
2. Theory
2.1 . Gas Hydrates
Natural gas hydrates are solid crystalline
compounds, resembling ice or wet snow in
appearance, but much less dense than ice.
Natural gas hydrates are formed when natural
gas component, notably methane, ethane,
propane, isobutene, hydrogen sulfide, carbon
dioxide and nitrogen enter the water lattice
(which is looser than the ice lattice) and occupy
the vacant lattice positions, causing the water
to solidify at temperatures considerably higher
than the freezing point of water. Enough
gaseous molecules must enter the lattice and
occupy the void to stabilize the lattice crystal
(Kumar, 1987).
Four conditions are required to form
hydrates (Sloan, Introductory overview:
Hydrate knowledge development, 2004):
1- Low temperature (commonly less than
300 K)
2- High pressure (greater than 38 bar
hydrostatic pressure at 277 K)
3- A non-polar guest molecule smaller than
0.9 nm, such as methane
4- Water.
Hydrates are classified by the arrangement
of the water molecules in the crystal, and
hence the crystal structure. Two types of
hydrates are commonly encountered in the
petroleum business: Type I and Type II,
sometimes referred to as Structure I and II. A
third type of hydrate that also may be
encountered is Type H (also known as
Structure H), but it is much less common
(Carroll, 2009).
Some of the common Type I hydrate
formers include methane, ethane, carbon
dioxide, and hydrogen sulfide. Among the
common Type II formers in natural gas are
nitrogen, propane, and isobutene.
2.2 . The Methods for Predicting Gas
Hydrate Formation
The first problem when designing processes
involving hydrates is to predict the conditions
of pressure and temperature at which hydrates
will form (Carroll, 2009).
The best method for determining conditions
of hydrate formation is to experimentally
measure the formation at the temperature,
pressure and composition of interest. Because
it is impossible to satisfy the infinite number of
conditions for which measurements are
needed, hydrate formation prediction methods
are needed to interpolate between
measurements (Heydari, Shayesteh, &
Kamalzadeh, 2006).
Methods to Predict Hydrate Formation
include graphical calculations, empirical
correlations, thermodynamic models and
software packages. In this study the empirical
correlations have been reviewed.
2.3 . Empirical Correlations
In | 1934, | Hammerschmidt | proposed | a |
correlation for gas hydrate formation, shown in | ||||
Eq. 1(Hammerschmidt, 1934). | (1) |
Where P is in PSI, T is in Fahrenheit. This
equation is simple and does not take into
account the effect of gas specific gravity.
Evaluation of Empirical Correlations for Predicting Gas Hydrate Formation Temperature 17
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In 1986, Berg proposed two T-explicit
correlations (Berge, 1986). For 1.55 ≤ γ < 1.58:
(2)
* +
And for 1.58 ≤ γ ≤ 2:
, (3)
* +-
*
( )+
For equation (2), P is in PSI, T is in
Fahrenheit but for equation (3), P is in kPa, T
is in Fahrenheit.
It should be noted that Berg notified PSI
and Fahrenheit as the units of equation (2) in
his article, but since the use of these units
showed Unreasonable results, different units
have been tested and Considering to the units
of some authors have been used in their article
for this equation, Finally the correct units of
this equation were discovered.
In 1991, Motiee suggested Eq. 4 for natural
gas mixtures (Motiee, 1991):
(4) |
Where P is in PSI, T is in Fahrenheit.
In 2005, Towler and Mokhatab proposed a
relatively simple equation for estimating
hydrate temperatures as a function of the
pressure and the gas gravity (Towler &
Mokhatab, 2005):
(5) |
Where P is in PSI, T is in Fahrenheit.
In 2009, Bahadori and Vuthaluru presented
one correlation for estimating HFT and
onecorrelation for estimating HPT (Bahadori,
2009):
(6)
(7)
where P is the pressure in kPa and T is the
temperature in K.
Depending on the ranges of pressure,
temperature and gas molecular weight,
different sets of adjustable parameters have
been recommended. Totally any of these
equations have 16 adjustable parameters.
In 2015, Safamirzaei proposed a T-explicit
correlation for 1.55 ≤ γ ≤ 2(Safamirzaei M. ,
2015):
(8)
Where:
A=194.681789
B=0.044232
C=0.189829
In this equation, P is in kPa and T is in K.
In addition to the introduced equations,
there are other equations such as Kobayashi
(Kobayashi, Song, Sloan , & Bradley, 1987),
Ameripour and Barrufet (Ameripour &
Barrufet, 2009) and etc.
The main advantages of these empirical
correlations are portability and simplicity.
Indeed, required input data are accessible and
they are applicable even with a simple
calculator. The results are in excellent
agreement with the experimental data in most
cases and even better than the results from
commercial simulators in some cases.
Despite of many advantages, these
correlations have some limitation. For
example, most of them can be used in the
defined ranges of pressure, temperature and
gas molecular weight and for the other ranges,
show high errors. Also, some of them are
accurate only for sweet natural gas mixtures or
some of them work quite well for pure formers.
There are some equations which have been
implemented by the artificial neural network
(ANN) (Zahedi, Karami, & Yaghoobi, 2009)
(Elgibaly & Elkamel, 1998) (Khamehchi,
Shamohammadi, & Yousefi, 2013). These
equations are often complicated and are not
suitable for calculations performed by hand
(Safamirzaei M. , 2015).
3. Analysis Method
In this study, more than 2000 experimental
data collected from literature (Guo &
Ghalambor, 2005) (Sloan & Koh, Clathrate
Hydrates of Natural Gases, 2007), and some of
empirical correlations have been evaluated for
these data separated in three groups:
1- Simple natural gas components included
methane, ethane, propane, is obutane, carbon
dioxide, nitrogen, and hydrogen sulfide.
18 Gas Processing Journal, Vol. 6, No. 1, 2018
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2- Binary guest mixtures
3- Gas mixture similar to natural gas
Evaluated empirical correlation included:
Motiee, Tolwer and Mokhatab,
Hammerschmidt, Safamirzaei, Bahadori, Berg
and new equation presented in this study.
For doing calculation the experimental
hydrate pressure and specific gravity of a
composition has been put into an equation.
Then calculated temperature has been
compared to experimental temperature for
calculating the accuracy of the equation.
In this study, average relative deviation
(ARD) and average absolute deviation (AAD)
have been implemented to assess different
equations deviations.
∑ (9)
∑ |
(10)
The results of evaluating have been
presented in tables 1-4 and Figures 1-15 in the
next section.
Since some of the equations have
temperature, pressure, or specific gravity
restrictions, so some experimental data may
not be used for some equations. The NOD1
column in tables represents the number of
data that can be used in the corresponding
equation.
By using experimental data and a simple
mathematic model, a new equation is
presented here for estimating HFT as a
function of gas pressure and specific gravity.
This equation is developed by fitting a
polynomial function to 100 experimental data
pointsusing curve fitting of MATLAB software.
This equation has 3 adjustable parameters:
(11)
where P is the pressure in kPa and T is the
temperature in K.
The R-squared value for this equation is
0.9988.
4. Discussion
4.1. Comparison the Results of the
First Group Data
The result of comparison the experimental
temperatures with temperatures calculated by
1 Number of Data
the equations for the first group of data are
plotted in graphs which are shown in Figures
1-9.
Figure1 shows that for the pressures above
200 MPa, proposed empirical correlation in the
present study and Towller and Mokhatab
(Towler & Mokhatab, 2005) equation presents
the closest results to experimental data.
For pressures lower than 200 MPa, Motiee
(Motiee, 1991) and Bahadori's (Bahadori, 2009)
represent the most accurate results.
Figure 2 shows hydrates formation
temperature for ethane in low pressures. It can
be seen that proposed empirical correlation in
the present study and Motiee equation provide
the best coresponding. For high pressure,
Figure 3 is applicable.
According to Figure4, for pressures above
1000 kPa, Hammerschmidt equation
(Hammerschmidt, 1934) calculated the
temperature of the propane hydrate formation
accuracy. For pressures less than 1000 kPa,
proposed empirical correlation in the present
study and Safamirzaei equation (Safamirzaei
M. , 2015) are in good agreement with the
experimental data. With respect to Figure 5,
for pressures higher than 0.893 MPa,
Hammerschmidt equation and for lower
pressures, proposed empirical correlation in
the present study shows the best fit with
experimental data.
Figure 6 shows for pressures lower than
900 kPa, Motiee and proposed empirical
correlation in the present study always provide
the most accurate temperatures for isobutane
hydrates. For pressures higher than 900 kPa
and lower than 50 kPa, Hammerschmidt
equation shows good performance.
Figure7 can be divided into several parts
and in each section, Motiee or Safamirzaei
equations is selected for calculations the
Nitrogen hydrate formation temperature.
According to Figure8, for hydrogen sulfide
at pressures below 57 kPa, Motiee and
Safamirzaei equations are almost correspond
with experimental data. For the pressure
between 57 to 90 kPa, proposed empirical
correlation in the present study shows very
satisfactory results. Towller and Mokhatab
equation is the best equations for pressures
higher than 90 kPa.
Figure 9 shows for the pressures below
3385 kPa, Motiee equation (Motiee, 1991) is
the best, and for higher pressures,
Hammerschmidt equation (Hammerschmidt,
1934) and proposed empirical correlation in
the present study provide good results for
carbon dioxide.
Evaluation of Empirical Correlations for Predicting Gas Hydrate Formation Temperature 19
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Figure 1. Comparison of the experimental temperature of hydrate formation with the results calculated by
equations for methane.
250
270
290
310
330
350
370
390
410
0 200 400 600 800 1000 1200
T(K)
P(MPa)
Experimental Motiee Towler&Mokhatab
Hammerschmit Safamirzaei proposed equation
Bahadori
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Figure 2. Comparison of the experimental temperature of hydrate formation with the results calculated by
equations for ethane at low pressure.
230
240
250
260
270
280
290
300
0 1000 2000 3000 4000 5000 6000 7000 8000
T(K)
P(kPa)
Experimantal Motiee Towler&Mokhatab Hammerscmit
Safamirzaei Berge Proposed Equation
Evaluation of Empirical Correlations for Predicting Gas Hydrate Formation Temperature 21
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Figure 3. Comparison of the experimental temperature of hydrate formation with the results calculated by
equations for ethane at high pressure.
250
260
270
280
290
300
310
320
330
340
0 100 200 300 400 500 600
T(K)
P(MPa)
Experimental Motiee Towler&Mokhatab Hammerschmidt
Safamirzaei Berge Proposed Equation
4MPa |
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Figure 4. Comparison of the experimental temperature of hydrate formation with the results calculated by
equations for propane at low pressure.
235
245
255
265
275
285
295
305
0 1000 2000 3000 4000 5000 6000 7000
T(K)
P(kPa)
Experimental Motiee Towler&Mokhatab
Hammerschmidt Safamirzaei Proposed Equation
Evaluation of Empirical Correlations for Predicting Gas Hydrate Formation Temperature 23
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Figure 5. Comparison of the experimental temperature of hydrate formation with the results calculated by
equations for propane at high pressure.
240
250
260
270
280
290
300
310
320
0 2 4 6 8 10 12 14 16 18
T(K)
P(MPa)
Experimantal Motiee Towler&Mokhatab Hammerschmidt Safamirzaei Proposed Equation
0.89 | 3MPa |
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Figure 6. Comparison of the experimental temperature of hydrate formation with the results calculated by
equations for Isobutane.
170
190
210
230
250
270
290
310
0 1000 2000 3000 4000 5000 6000
T(K)
P(kPa)
Experimental Motiee Toewler&Mokhatab
Hammerscmit Safamirzaei Proposed Equation
Evaluation of Empirical Correlations for Predicting Gas Hydrate Formation Temperature 25
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Figure 7. Comparison of the experimental temperature of hydrate formation with the results calculated by
equations for nitrogen.
270
290
310
330
350
370
390
0 50 100 150 200 250 300 350 400 450 500
T(K)
P(MPa)
Experimantal Motiee Towler&Mokhatab Hammerscmit
Safamirzaei Berge Proposed Equation
207 MPa |
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Figure 8. Comparison of the experimental temperature of hydrate formation with the results calculated by
equations for hydrogen sulfide.
Figure 9. Comparison of the experimental temperature of hydrate formation with the results calculated by
equations for carbon dioxide.
246
256
266
276
286
296
0 500 1000 1500 2000 2500
T(K)
P(kPa)
Experimental Motiee Towler&Mokhatab
Hammerschmidt Safamirzaei Proposed Equation
255
260
265
270
275
280
285
290
295
300
2000 2500 3000 3500 4000 4500 5000
T(K)
P(kPa)
Experimental Motiee Towler&Mokhatab Hmmerschmidt Safamirzaei Proposed Equation
90kPa | |
5 | 7kPa |
3385kPa |
Evaluation of Empirical Correlations for Predicting Gas Hydrate Formation Temperature 27
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4.2. Comparison the Results of the
Second Group Data
Figures 10 through 13 show the calculated
result in compared to experimental data. The
curves of equations that show a large deviation
have been omitted.
According to table 2 and Figure 15, it can
be seen that Hammerschmidt
(Hammerschmidt, 1934) presents the best
result for ethane-containing mixtures, so it is
not necessary to plot the graph. This is true for
the mixtures containing Normal butane. The
reason for superiority of Hammerschmidt
equation for these mixtures may be due to the
fact that ethane, propane, and isobutane
molecules only enter the large cages of their
respective hydrate. And in the large cages,
there is a high degree of occupancy. So, for
ethane, propane, and isobutane, the
composition of the hydrate does not appear to
be a function of the temperature or the
pressure.
On the other hand, Hammerschmidt
equation is the only equation in which the
molecular weight of the component is not
affected, so it is expected that this equation
gives good results for these compounds. As
shown in table 2, Hammerschmidt equation for
Propane also has a very good result.
Figure 10. Comparison of the experimental temperature of hydrate formation with the results calculated by
equations for mixtures containing propane at low pressures.
230
240
250
260
270
280
290
300
0 500 1000 1500 2000 2500 3000 3500 4000 4500
T(K)
P(kPa)
Experimental Hammershmidt Safamirzaei Proposed Equation
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Figure 11. Comparison of the experimental temperature of hydrate formation with the results calculated by
equations for mixtures containing propane at high pressures.
265
270
275
280
285
290
295
300
305
310
0 2 4 6 8 10 12 14 16 18 20
T(K)
P(MPa)
Experimental Hammerscmidt Safamirzaei Proposed Equation
Evaluation of Empirical Correlations for Predicting Gas Hydrate Formation Temperature 29
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Figure 12. Comparison of the experimental temperature of hydrate formation with the results calculated by
equations for mixtures containing isobutane.
255
260
265
270
275
280
285
290
295
0 500 1000 1500 2000 2500 3000 3500
T(K)
P(kPa)
Experimental Hammerschmidt Proposed Equation
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Figure 13. Comparison of the experimental temperature of hydrate formation with the results calculated by
equations for mixtures containing nitrogen.
4.3. Comparison of the Results of the
Third Group Data
Due to the high density of data, use of the
diagram is not suitable and it is better to use
the results of calculations presented in table 3.
4.4. Conclusion about Empiricalequations
4.4.1. Motiee
This equation is applied for natural gas
mixtures. As shown in table 1 and Figure 14,
for pure ethane and nitrogen, presents the best
results and for pure methane is one of the best,
but for pure propane and butane shows high
deviations. The reason for is that Motiee
equation is presented for natural gas, and the
presence of propane and butane in pure form,
displaces the sample from the natural gas
mixture.
Table 4 shows that for the mixture of
methane and ethane, Motiee calculates the
most exact result. This equation is relatively
accurate for gas mixture similar to the natural
gas but for binary gas mixtures according to
table 2, the results show high errors. Since
that this equation has no limitations for
pressure, temperature or gas molecular
weight, it has been applied for all the
experimental points used in this paper.
4.4.2. Towler and Mokhatab
This equation has no limitation like Motiee.
According to the tables, this equation has
always reported moderate results and this is
one of the most important advantages of this
equation.
4.4.3. Hammerschmidt
The equation represented by Hammerschmidt
is very simple and has only two parameters.
Since that this equation has no limitations for
pressure, temperature or gas molecular
weight, it has been applied for all the
experimental points used in this paper.
Tables 1 and 2 show that the performance
of this equation for binary gas mixtures is
better than pure compounds. So for the
mixture of ethane, butane or nitrogen with
other compounds it presents the best result.
4.4.4. Safamirzaei
This equation is presented for natural gas
mixtures (1.55 ≤ γ ≤ 2), but has been evaluated
for heavier hydrocarbon mixtures in this study.
250
260
270
280
290
300
310
0 5 10 15 20 25 30 35
T(K)
P(MPa)
Experimental Motiee Hammershmidt Proposed Equation
Evaluation of Empirical Correlations for Predicting Gas Hydrate Formation Temperature 31
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As shown in table 3, for the natural gas
mixtures, Safamirzaei presents the best result
compared to other equations. Also, for pure
propane and butane, or mixtures containing
propane with other compounds, the results are
excellent. The weakness of this equation is for
pure nitrogen and pure sulfide, or mixtures
containing them.
4.4.5. Bahadori
These correlations cover molecular weight
between 16 to 29 and temperatures between
265 to 298 K as well as pressures between
1200 to 40000 kPa. As shown in tables 1, 2 and
4, for pure methane, mixture of methane and
ethane, as well as mixtures similar to natural
gas, Bahadori has presented the best results.
Due to temperature, pressure and gas
molecular weight limitations for these
equations, most of the data used in this article
is not usable. The error of this equation results
increase with decreasing purity of methane in
the mixtures.
4.4.6. Berge
This equation is for 1.55 ≤ γ ≤ 2, therefore does
not work for methane, propane, butane and
pure hydrogen sulfide, and mixtures whit gas
molecular weight out of this range. As shown
in table 1, for pure nitrogen, after the Motiee,
Berge shows the best result.
4.4.7. Proposed Empirical Correlation in
the Present Study
This equation has no limiting conditions and
according to table1, for pure propane and
isobutane, presents the best results and for
pure methane and ethane is one of the best
results. Also, for binary guest mixtures
containing ethane, propane or nitrogen and
other compounds, the results are more
accurate than other equations. For mixtures
similar to the natural gas, according to table 3,
this equation presents acceptable results. This
equation is evaluated for all the experimental
points used in this paper and often presents
one of the three accurate results.
Table 1. Comparison of calculated result for simple natural gas components
Carbon
Dioxide
Hydrogen
Methane Ethane Propane Isobutane Nitrogen sulfide
ARDNOD
(%)
AAD
AAD (K) ARD (%) NOD AAD (K) ARD (%) NOD AAD (K) ARD (%) NOD AAD (K) ARD (%) NOD AAD (K) ARD (%) NOD AAD (K) ARD (%) NOD (K)
Motiee | 7.35 | 2.5 | ||||||||||||||||||
Mokhatab | 8.29 2.95 | |||||||||||||||||||
Hammerschmidt 24.03 8.03 | ||||||||||||||||||||
SafaMirzaei | 8.42 2.92 | |||||||||||||||||||
Bahadori | 3.54 1.27 174 | - | - | 0 | - | - | 0 | - | - | 0 | - | - | 0 | - | - | 0 | - | - | 0 | |
Berge | - | - | 0 | 7.29 2.48 | 65 | - | - | 0 | - | - | 0 | - | - | 0 | - | - | 0 | - | - | 0 |
271 4.24 0.69 65 23.50 8.53 107 84.81 31.22 59 12.75 4.52 96 13.60 4.71 29 14.55 5.23 32
271 8.32 2.85 65 7.81 2.84 107 6.53 2.44 59 23.66 8.24 96 8.59 2.98 29 23.15 8.59 32
271 18.67 6.27 65 6.31 2.30 107 7.64 2.83 59 38.92 13.32 96 13.19 4.55 29 11.5 4.32 32
271 6.07 2.1 65 5.95 2.15 107 4.05 1.48 59 17.99 6.31 96 10.46 3.65 29 22.4 8.34 32
8.10 2.84 271 4.39 1.49 65 4.36 1.60 107 4.06 1.54 59 16.77 5.84 96 10.18 3.53 29 16.76 6.24 32
proposed
empirical
correlation in
the present
study
Table 2. Comparison of calculated result for binary guest mixtures
Nitrogen +
another
component
n-Butane +
another
component
Isobutane +
another
component
Propane +
another
component
Ethane + another
component
Methane +
another
component
ARD NOD
(%)
AAD
AAD (K) ARD (%) NOD AAD (K) ARD (%) NOD AAD (K) ARD (%) NOD AAD (K) ARD (%) NOD AAD (K) ARD (%) NOD (K)
Motiee | 13.86 | ||||||||||||||||
Mokhatab | 7.91 | ||||||||||||||||
Hammerschmidt 7.30 | |||||||||||||||||
Safa Mirzaei Bahadori Berge |
7.31 5.80 7.40 |
2.69 | 310 | - | - | 0 | 11.63 4.14 | 13 | - | - | 0 | - | - | 0 | - | - | 0 |
5.19 658 6.89 2.47 132 23.38 8.48 232 34.69 12.64 57 20.81 7.542 21 14.41 5.19 63
3.08 658 10.20 3.71 132 9.57 3.49 232 9.68 3.50 57 15.27 5.53 21 19.77 7.13 63
2.85 658 3.92 1.44 132 5.07 1.87 232 3.21 1.16 57 3.08 1.16 21 13.73 4.96 63
2.87 658 9.60 3.50 132 7.71 2.79 232 7.79 2.81 57 13.90 5.27 21 18.42 6.64 63
2.65 402 - - 0 9.02 3.19 25 - - 0 - - 0 21.05 7.62 21
6.07 2.19 658 6.24 2.19 132 4.38 1.70 232 4.59 1.66 57 9.52 3.45 21 14.21 5.13 63
proposed
empirical
correlation in
the present
study
32 Gas Processing Journal, Vol. 6, No. 1, 2018
GPJ
Table 3. Comparison of calculated result for gas mixture similar to natural gas
Similar to Natural Gas
(Guo & Ghalambor, 2005)
Similar to Natural Gas
(Sloan & Koh, Clathrate
Hydrates of Natural Gases, 2007)
AAD (K) %ARD NOD AAD (K) %ARD NOD
Motiee 1.92 0.67 125 1.13 0.399 53
Mokhatab 1.18 0.41 125 1.86 0.64 53
Hammerschmidt 2.72 0.93 125 4.31 1.50 53
Safa Mirzaei 1.06 0.37 125 1.24 0.43 53
Bahadori 1.31 0.46 102 0.66 0.23 41
Berge 4.48 1.60 125 5.23 1.87 45
proposed empirical correlation in 1.32 0.46 125 1.81 0.64 53
the present study
Table 4. Comparison of calculated result for methane and ethane mixture
Methane + Ethane
(Elgibaly & Elkamel, 1998)
AAD (K) %ARD NOD
Motiee 1.06 0.37 30
Mokhatab 2.93 1.04 30
Hammerschmidt 5.03 1.77 30
Safa Mirzaei 2.56 0.91 30
Bahadori 1.36 0.48 27
Berge 2.80 1.01 30
proposed empirical correlation in the present study 2.78 1.00 30
2.84 2.92 2.5 2.95 A |
8.03 |
RD% |
Methane |
Proposed Equation Bahadori SafaMirzaei Hammerschmidt Motiee Mokhatab |
1.6 2.15 2.3 2.85 |
8.53 |
RD% |
Propane |
Proposed Equation SafaMirzaei Hammerschmidt Motiee Mokhatab |
1.27
8 6 4 2 0
10
1.49 2.48 2.1 6.27 0.69 2.85 7 6 5 4 3 2 1 0 ARD% Ethane Proposed Equation Berge SafaMirzaei Hammerschmidt Motiee Mokhatab |
1.54 1.48 2.83 31.22 2.44 0 10 20 30 40 ARD% Isobutane Proposed Equation SafaMirzaei Hammerschmidt Motiee Mokhatab |
8 6 4 2 0
10
Evaluation of Empirical Correlations for Predicting Gas Hydrate Formation Temperature 33
GPJ
2.19 AR |
2.87 2.85 3.08 2.69 D% |
5.19 |
Methane + another component |
Proposed Equation Berge SafaMirzaei Hammerschmidt Motiee Mokhatab Bahadori |
2.65 6 5 4 3 2 1 0
2.19 D% |
3.5 3.71 |
1.44 AR |
2.47 |
Ethane + another component |
Proposed Equation SafaMirzaei Hammerschmidt Motiee Mokhatab |
0
0.5
1
1.5
2
2.5
3
3.5
4
1.7 3.19 2.79 1.87 |
8.48 |
3.49 4.14 ARD% |
Propane + another component |
Proposed Equation Berge SafaMirzaei Hammerschmidt Motiee Mokhatab Bahadori |
8 6 4 2 0
10
1.66 2.81 1.16 |
12.64 |
3.5 A |
RD |
% |
Isobutane + another component |
Proposed Equation SafaMirzaei Hammerschmidt Motiee Mokhatab |
8 6 4 2 0
10
12
14
Figure 14. Comparison of calculated result for simple natural gas components
3.53 2.98 |
4.55 |
4.71 Sulfide Hydrogen |
RD% |
Proposed Equation SafaMirzaei Hammerschmidt Motiee Mokhatab |
3.65
5 4 3 2 1 0
5.84 6.31
13.32
4.52
8.24
8 6 4 2 0
10
12
14
ARD%
Nitrogen
Proposed Equation SafaMirzaei
Hammerschmidt Motiee
Mokhatab
34 Gas Processing Journal, Vol. 6, No. 1, 2018
GPJ
3.45
5.27 D% |
1.16 |
7.542 n-Butane + another component |
5.53 |
AR |
Proposed Equation SafaMirzaei Hammerschmidt Motiee Mokhatab |
8 6 4 2 0
5.13 4.96 5.19 D% |
6.64 7.13 |
AR |
Nitrogen + another component |
Proposed Equation SafaMirzaei Hammerschmidt Motiee Mokhatab |
8 6 4 2 0
Figure 15. Comparison of calculated result for binary guest mixtures
5. Conclutions and Recommendation
In this study, the methods and empirical
correlations have been reviewed and their
predictive capabilities have been evaluated
with the use of more than 2000 experimental
data collected from the literature. These data
have been separated in three groups: (1)
simple natural gas components included
methane, ethane, propane, isobutane, carbon
dioxide, nitrogen, and hydrogen sulfide (2)
binary gas mixtures and (3) gas mixture
similar to natural gas. After expressing the
restriction of each empirical correlation
included Motiee, Tolwer and Mokhatab,
Hammerschmidt, Safamirzaei, Bahadori, Berg
and proposed empirical correlation in the
present study, the results of evaluating have
been presented in several tables and curves.
It is clear that each empirical equation has
some limitations. In some cases, in addition to
the specific gravity of the mixture, its
composition and purity of the components also
has a significant effect on some of the results.
It is possible an equation covers intended
molecular weight, but the result is not
accurate which may be related to the lack of
purity of component, the presence of some sour
compounds, and so on.
Sometimes the average absolute deviation
(AAD) for a group of experimental data is the
minimum but it doesn’t mean this equation is
superior to other equations since it is seen; the
maximum deviation is related to this equation.
For this reasons, precautions should be taken
in using the equations. It is preferred to apply
all the suitable equation for a given point.
According to this study, for pure methane,
mixture of methane and ethane, as well as
mixtures similar to natural gas, Bahadori has
presented the perfect results. Safamirzaei
provides the most accurate equation for the
natural gas mixtures.
For the mixture of ethane, butane or
nitrogen with other compounds,
Hammerschmidt presents the precisest result.
Motiee calculates the most exact result for the
mixture of methane and ethane.
The proposed empirical correlation in the
present study has shown reliable performance
for both simple natural gas components and
mixtures. Despite the existence three
adjustable parameters, the accuracy of this
equation shows the ranking 1 to 3 compare to
the rest of the equations.
Since the type of hydrate formed depends
on their former and each of the equation
provides the best results for a particular group
of compounds, it is proposed to investigate the
relationship between the type of hydrate and
the equations
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formation pressures or temperatures
for systems with or without inhibitors.
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