Document Type : Research Paper
Authors
Department of Petroleum Engineering, Petroleum University of Technology, Ahwaz, Iran
Iranian Journal of Oil & Gas Science and Technology
,
Vol. 4 (2015), No. 2, pp. 40-49
http://ijogst.put.ac.ir
Developing a Fuzzy Logic Model to Predict Asphalten
e Precipitation
during Natural Depletion based on Experimental Data
Mobina Mohammadi, Riyaz Kharrat
*
, and Abdonabi Hashemi
1
Department of Petroleum Engineering, Petroleum Uni
versity of Technology, Ahwaz, Iran
Received:
October 05, 2013
; revised:
October 12, 2014
; accepted:
October 27, 2014
Abstract
Although the asphaltene problems have been studied
for many years, there are numerous controversial
issues around the nature of asphaltene. Since aspha
ltene precipitation imposes significant costs on oi
l
industry, a comprehensive research must be done to
address the issues about asphaltene structures. It
is extremely important to investigate the behavior
of asphaltene precipitation and ways to minimize it
under changeable effective thermodynamic factors su
ch as pressure, temperature, and composition.
In this work, natural depletion tests were performe
d at three different temperatures of 200, 170, and
135 °F on Iranian heavy oil samples. At each step o
f the experiments, IP 143 standard test was used to
measure the precipitated asphaltene. Then, a fuzzy
logic model capable of predicting asphaltene
precipitation in a range of temperatures was develo
ped. The fuzzy logic model predicts experimental
data accurately. The obtained results were finally
compared with a solid model using the commercial
software implementing the mentioned model, and it w
as concluded that there was good agreement
between the fuzzy logic model and the simulation re
sults.
Keywords:
Asphaltene Precipitation, Natural Depletion, Fuzzy
Logic, Solid Model
1. Introduction
Asphaltenes, often defined by their solubility char
acteristics, are materials insoluble in n-heptanes
at a
dilution ratio of 40 parts to one part crude oil an
d re-dissolve in toluene (Speight et al., 1985). Th
e
prediction of asphaltene precipitation during oil p
roduction is an important issue, because it may
cause plugging of the formation, wellbore, and prod
uction facilities and increase the cost of oil
production. There are two different models to descr
ibe the nature of asphaltenes in solution. The firs
t
approach is the solubility model, which considers a
sphaltenes as dissolved in a liquid state. Accordin
g
to this model, the asphaltenes totally dissolve in
crude oil and form a uniform solution (Burke et al.
,
1990). The second approach is the colloidal model,
which considers asphaltenes as solid colloidal
particles suspended in crude oil and stabilized by
large resin molecules (Leontaritis and Mansoori,
1997). Recent studies confirm that asphaltene preci
pitations increase when temperature decreases; this
can be interpreted as a result of variation in volu
me fraction of the species when temperature changes
(Afshari et al., 2010). Although these models predi
ct asphaltene deposition well, they need fluid
characterization and rigorous calculation of phase
behavior. The aim of this work is to develop a fast
,
simple, and accurate fuzzy model to predict the asp
haltene deposition.
*
Corresponding Author:
Email: kharrat@put.ac.ir
M. Mohammadi et al. / Developing a Fuzzy Logic Mode
l to Predict Asphaltene ...
41
Fuzzy-set theory, which was developed by Zadeh in 1
965, is a great tool for modeling the uncertainty
associated with ambiguity, imprecision, and lack of
information (Ross, 1995). Fuzzy logic achieves
this important task through fuzzy sets. In classica
l bivalent sets (crisp sets), an object either belo
ngs to
a set or it does not. Unlike the crisp sets, in fuz
zy sets, everything is a matter of degrees. Therefo
re, an
object belongs to a set to a certain degree (Mohagh
egh, 2000). Fuzzy logic has four foundations
including fuzzy sets, membership functions (MF), fu
zzy rules, and logical operations.
Fuzzy inference system (FIS) involves all of these
four foundations to formulate the mapping from
input to output using fuzzy logic. The determinatio
n of the exact fuzzy rules and the type and number
of membership functions for a specific problem is a
difficult task and requires extensive testing.
Fuzzy logic has many applications in oil industry s
uch as enhanced oil recovery (Nikravash et al.,
1997), well stimulation (Zoveidavianpoor et al., 20
12), and underbalanced drilling (Garrouch and
Lababidi, 2001). Specifically, fuzzy logic has also
been used for the prediction of asphaltene
deposition (Ebadi et al., 2012); however, it is dif
ferent from this work, since, in this paper, the
observed data are obtained by carrying out experime
nts for better understanding the asphaltene
behavior of the reservoir fluid when temperature an
d pressure change. One of the advantages of this
work is the use of an experimental data set to prov
ide a guideline of the asphaltene behavior within
the fluid and to define more precise fuzzy rules. F
urthermore, the fuzzy logic model is validated by
comparing its results with those of a solid model.
In this work, a fuzzy logic model was developed to
predict asphaltene precipitation behavior during
natural depletion based on experimental data. Then,
the fuzzy logic model was utilized for predicting
asphaltene precipitation at various temperatures, i
ncluding 130 and 180 °F. Finally, the obtained
results were compared with a solid model using comm
ercial software (CMG, WinProp module). The
precipitation of asphaltene phases in WinProp is mo
deled using a multiphase flash calculation in
which the fluid phases are described with an equati
on of state, and the fugacities of components in th
e
solid phase are predicted using the solid model
.
The solid phase may consist of one or more
components
.
The approach for modeling asphaltene precipitation
is described in detail elsewhere
(Nghiem et al., 1993; Nghiem et al., 1996). In the
solid model tried by Gupta (1986) and Thomas et
al. (1992), the precipitated asphaltene is represen
ted as a pure solid, while the oil and gas phases a
re
modeled with a cubic equation of state (EOS).
2. Experimental setup and procedure
2.1. Setup
A schematic of the experimental setup is shown in F
igure 1. It consists of a hydraulic pump, a heating
system, a high pressure 0.5
μ
m metal filter, a PVT cell, a transfer vessel, a pr
essure transducer, a
sampler, lines, and several pressure gauges. The te
sts were started at reservoir pressure and
temperature of 4470 psia and 200 °F respectively. T
able 1 shows the reservoir fluid composition and
Table 2 summarizes the properties of the reservoir
fluid.
42
Iranian Journal of Oil & Gas Science and Technolog
y,
Vol. 4 (2015), No. 2
Figure 1
High pressure-high temperature apparatus.
Table 1
Reservoir oil composition.
C o mp on en ts
R e s e rv oi r Oil Co mpo si ti on ( M ol e % )
H
2
S
0.00
N
2
0.39
CO
2
1.74
C
1
20.55
C
2
7.31
C
3
5.34
iC
4
1.00
nC
4
3.65
iC
5
3.10
nC
5
4.75
C
6
5.48
C
7
3.23
C
8
1.32
C
9
2.27
C
10
2.19
C
11
1.81
C
12+
35.87
M. Mohammadi et al. / Developing a Fuzzy Logic Mode
l to Predict Asphaltene ...
43
Table 2
Reservoir oil properties.
Property
Value
API
20.32
Total AS content (wt. %)
12.80
GOR (SCF/STB)
319.04
Reservoir pressure (psia)
4470.00
Saturation pressure (psia)
1433.70
Reservoir temperature (ºF)
200.00
Molecular weight of residual Oil
269.00
Molecular weight of C
12+
fraction
370.00
Molecular weight of reservoir oil
169.00
Specific gravity of C
12+
fraction @ 60/60 ºF
0.98
2.2. Procedure
The experiments were conducted by transferring the
heavy oil into the PVT cell. Pressure depletion
tests, including four or five pressure steps, start
ed at reservoir pressure. Three different temperatu
res
were selected to investigate the effect of temperat
ure on asphaltene precipitation. After reaching
equilibrium conditions at a specific pressure and t
emperature, the soluble part of asphaltene was
transferred to the sampler by filter. The asphalten
e precipitation in PVT cell was obtained by
subtracting flashed oil asphaltene precipitation fr
om initial asphaltene content. Standard IP 143 test
was used to measure asphaltene content at each pres
sure step.
3. Result and discussion
3.1. Natural depletion
The results of natural depletion test for three tem
peratures are shown in Figure 2. As it can be seen
in
the figure, above the bubble point pressure, as the
pressure decreases, the asphaltene precipitation
increases; this is because of the dominancy of the
solubility model. However, because the colloidal
model is dominant below the bubble pressure, asphal
tene precipitation decreases as the pressure
declines.
Figure 2
Results of natural depletion test at different temp
eratures.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0
1000
2000
3000
4000
5000
6000
7000
8000
Asphaltene (wt.%)
Pressure (psia)
Well A:T=200
⁰
F
Well A:T=170
⁰
F
Well A:T=135
⁰
F
44
Iranian Journal of Oil & Gas Science and Technolog
y,
Vol. 4 (2015), No. 2
3.2. Fuzzy logic model
The experimental results of natural depletion were
used to develop fuzzy rules and the fuzzy logic
model. In this model, there are two input parameter
s, namely pressure and temperature, and one
output, i.e. asphaltene precipitation in the PVT ce
ll. Membership function
(MF) is a curve that defines
how each point in the input space is mapped to a me
mbership value (or degree of membership
between 0 and 1). The Gaussian membership function,
because of its highly accurate prediction, has
been selected in this work. There are three members
hip functions for temperature input, including
low, moderate, and high (Figure 3). Six membership
functions were defined for pressure input,
including very low, low, moderate, high, very high,
and extremely high (Figure 4). Further six
membership functions including null, low, moderate,
high, sever, and extremely severe were selected
for the output (Figure 5).
Fourteen fuzzy rules and Mamdani fuzzy interference
system (FIS) were utilized to develop the
model. Figure 6 shows a three dimension diagram of
pressure-temperature-asphaltene response of the
model.
Figure 3
Membership function of temperature.
Figure 4
Membership function of pressure.
0.0
0.2
0.4
0.6
0.8
1.0
110
130
150
170
190
210
Degree of Membership
Temperature ( ̊F)
Low
Moderate
High
0.0
0.2
0.4
0.6
0.8
1.0
500
1500
2500
3500
4500
5500
Degree of Membership
Pressure (psia)
Very Low
Low
Moderate
High
Very High
Ext-High
M. Mohammadi et al. / Developing a Fuzzy Logic Mode
l to Predict Asphaltene ...
45
Figure 5
Membership function of asphaltene precipitation.
Figure 6
Three dimensional plot of pressure-temperature-asph
altene using the fuzzy logic model.
3.3. Comparison of the experimental and fuzzy model
results
The fuzzy model properly predicts experimental data
and the coefficient of determination is equal to
0.94625. Figure 7 shows the cross-plot of the fuzzy
model predictions and experimental data.
According to this figure, the fuzzy model is ready
to predict asphaltene precipitation at other pressu
res
and temperatures. The comparison of the experimenta
l data and the fuzzy logic prediction was
performed at three different temperatures including
200, 170, and 135 °F (Figures 8.a-8.c). Good
agreement between the experimental data and the fuz
zy model predictions is observed.
To test the generality of the developed model, the
fuzzy logic model was used to predict the
asphaltene weight percent versus pressure at other
temperatures such as 130 and 180 °F. At these
temperatures, the fuzzy logic results were compared
with a rigorous solid model using commercial
software and it was concluded that there were accep
table differences between the results of the fuzzy
logic models and those of the simulation (Figure 9)
.
0.0
0.2
0.4
0.6
0.8
1.0
0
0.5
1
1.5
2
2.5
Degree of Membership
Asphaltene Precipitation (wt.%)
Null
Low
Moderate
High
Severe
Ext-Severe
46
Iranian Journal of Oil & Gas Science and Technolog
y,
Vol. 4 (2015), No. 2
Figure 7
Fuzzy prediction data versus experimental data.
Figure 8.a
Comparison of experimental data and fuzzy predictio
n at T= 135 °F.
Figure 8.b
Comparison of experimental data and fuzzy predictio
n at T= 170 °F.
0.0
0.5
1.0
1.5
2.0
0.0
0.5
1.0
1.5
2.0
Outputs Y, Linear Fit: Y=0.92T+0.076
Targets T
Best Linear Fit
Y=T
Data Points
0.0
0.2
0.4
0.6
0.8
1.0
0
1000
2000
3000
4000
5000
Asphaltene (wt.%)
Pressure (psia)
Fuzzy Prediction
Experimental Results
0.0
0.3
0.6
0.9
1.2
1.5
1.8
0
1000
2000
3000
4000
5000
Asphaltene (wt.%)
Pressure (psia)
Fuzzy Prediction
Experimental Results
M. Mohammadi et al. / Developing a Fuzzy Logic Mode
l to Predict Asphaltene ...
47
Figure 8.c
Comparison of experimental data and fuzzy predictio
n at T= 200 °F.
Figure 9
Asphaltene weight percent versus pressure graph usi
ng commercial software and fuzzy logic prediction d
ata at
constant temperatures.
4. Conclusions
Natural depletion tests were carried out at three d
ifferent temperatures, i.e. 200, 170, and 135 °F. I
t
was observed that as the reservoir pressure decreas
es to the bubble point pressure, asphaltene
precipitation increases. Furthermore, as the pressu
re falls below the bubble point pressure, asphalten
e
precipitation decreases. Moreover, it is concluded
that the solubility model is dominant above the
bubble point pressure, and that the colloidal model
is dominant below the bubble point pressure. In a
further step, a fuzzy logic model was developed to
predict asphaltene precipitation during natural
depletion at other temperatures. It was shown that
there is good agreement between the experimental
data and the fuzzy logic model. The coefficient of
determination between the fuzzy model prediction
and the experimental data is close to unity (0.9462
5) confirming good accuracy in the predictions.
Finally, the fuzzy logic results were compared with
those of the solid model run using a commercial
software package ending up in acceptable agreement.
0.0
0.3
0.6
0.9
1.2
1.5
1.8
0
1000
2000
3000
4000
5000
Asphaltene (wt.%)
Pressure (psia)
Fuzzy Prediction
Experimental Results
0.0
0.3
0.6
0.9
1.2
1.5
1.8
0
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Asphaltene Precipitation (wt.%)
Pressure (psia)
WinProp Result (T=130 ̊F)
WinProp Result (T=180 ̊F)
Fuzzy Prediction (T=130 ̊F)
Fuzzy Prediction (T=180 ̊F)
48
Iranian Journal of Oil & Gas Science and Technolog
y,
Vol. 4 (2015), No. 2
Although fuzzy logic is a powerful tool for these k
inds of vague systems, there is no capability of
learning and pattern recognition in the fuzzy syste
m. To overcome this shortcoming, neurofuzzy
systems, which refer to the combinations of artific
ial neural networks and fuzzy logic, could be
considered as very useful alternatives in the petro
leum industry.
Nomenclature
MF
: Membership function
FIS
: Fuzzy inference system
EOS
: Equation of state
P
: Pressure
T
: Temperature
API
: American Petroleum Institute
GOR :Gas oil ratio
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