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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Volume 4, Issue 2

Spring 2015

Pages 40-49

**Receive Date:**05 October 2013**Revise Date:**12 October 2014**Accept Date:**27 October 2014