International Journal of Scientific & Engineering Research, Volume 6, Issue 4, April-2015 1316

ISSN 2229-5518

A Mathematical Model for Predicting Absolute Wax Thickness Distribution in Wellbores and Flow Lines

Akinade Akinwumi, Ajediti Omolola

ABSTRACT: Flow assurance governs the success of the fluid journey from reservoir to point of sale. Understanding this concept helps to ensure that any development plan—from exploration through abandonment—is technically viable and designed for optimal operations throughout the field's life. Flow assurance in sub-sea focuses on preventing solid deposits from blocking the flow path. The principal solids of concern are Wax and Hydrates, sometimes Scale and Asphaltenes can also be major threats to flow assurance that must be assessed by design teams. Controlling this solid deposits involves three main strategies; keeping the system pressure and temperature in a region where the solids are unstable (thermodynamic control) or controlling the conditions of solids formation so that deposit do not formed (kinetic control) or allowing solids to deposit, then periodically removing them (mechanical control).This research work is based on mechanical solid control strategies by developing a simple analytical model for predicting the absolute Wax thickness in a specified length of pipeline via the rheological properties of the flowing fluid. Apart from predicting wax thickness rate, this work can also be used to assess prevention and remediation strategies such as insulation effectiveness and pigging frequency during crude oil production.

Keywords: wax, flow assurance, hydrate, asphaltene, pigging.

.

INTRODUCTION

——————————  ——————————
Crude oils are mixture of light and heavy hydrocarbons. The components in crude oils can be classified into paraffin, naph- thene and aromatic components [1]. Though the non-n-alkane components in crude oils are minor, it is essential to consider the influence of non-alkane components in the model since their properties, such as fusion temperature and fusion en- thalpy, are much different from paraffin. The solubility of each component of crude oils depends on the temperature and composition of the system. When the temperature of crude oil drops, the solubility of the heavy fractions would be reduced and they will precipitate in forms of wax and asphaltene first [2]. There are problems caused by wax precipitation, such as the change in the flow behavior of crude oil from Newtonian to non-Newtonian, the decrease of production rates, the in- crease of energy consumed and the failure of facilities [4].
Paraffinic hydrocarbon fluids can cause a variety of problems in a production system ranging from solid stabilizes emulsion to a gelled flowline. Problem caused by wax occur when the fluid cools from reservoir conditions and wax crystal begin to form. The temperature at which crystals first begin to form is called the cloud point. At temperature below the cloud point, crystals begin to form and grow. Crystals may form either in the bulk fluid forming particles that are transported along with the fluid or deposit on a cold surface where crystals will

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• Akinade Akinwumi is currently pursuing PhD degree program in Petrleum Engineering in University of Ibadan, Nigeria. PH-08038090006. E-mail: akinchem2003@yahoo.com

• Ajediti Omolola is currently lecturing at Afe Babalola Univerty Ado-Ekiti,

Nigeria, she is pursuing PhD degree program in Petrleum Engineering in

University of Ibadan, Nigeria. PH-08063580655.E-mail: bus-

sy_omolola@yahoo.com
build-up and foul the surface “[1], [12],[13]”.
While there are numbers of problems that wax may cause in a production system, producers focus on two issues. The first issue is gel formation and the second issue is deposition. A crude oil gel forms when wax precipitates from the oil and forms a three dimensional structure spanning the pipe. This does not occur while the oil is flowing because the intermolec- ular structure is destroyed by shear forces as it is able to form. However, when the oil stops flowing wax particles will inter- act, join together and form a network resulting in a gel struc- ture if enough wax is out of solution “[16], [17]”.
In a pipe, wax deposition results in flow restriction or possibly a complete blockage. Complete blockage of flow due to depo- sition is rare. Most pipeline blockages occur when a pig is run through a pipeline after deposition as occurred and a signifi- cant deposit has built up. In this situation the pig will continue to scrape wax from the pipe wall and build up a viscous slug or candle in front of the pig. However, if the candle becomes too large there will be insufficient pressure for the pig to move. When this occurs the pig becomes stuck and mechanical intervention to remove the candle will be necessary before the pig can be moved ”[5], [8], [9], [10]”.
This research work is based on mechanical solid control strat- egies by developing a simple analytical model for predicting the absolute Wax thickness distribution in a specified length of pipeline via the rheological properties of the flowing fluid. Apart from predicting wax thickness rate, this work can also be used to assess prevention and remediation strategies such as insulation effectiveness and pigging frequency during crude oil production.

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International Journal of Scientific & Engineering Research, Volume 6, Issue 4, April-2015 1317

ISSN 2229-5518

2.0 MODEL FORMULATION

(A) Developing The Analytical Model

2− y 5− y y

   

Considering the frictional pressure drop component of energy
equation

∆p f

= 2ρlx

4q

 π

1 µ

   

   

(9)

Making d the subject of the formula

2ϕρu 2l

5 2ρlx  4q 

 

2− y

y

 µ 

 

. (10)

∆p f

=

gc d

(1)

∆p f

 π   ρ 

Let

τ w be wax thickness as shown below

The wax thickness inside a pipe section can be modeled by assuming a uniform deposition, through a horizontal flow in pipe i.e

τ w

τ w

q 4q

Since u = =

A π d 2

d

Substitute

u for in [1]

2

5− y

2ρlx  4q 

2− y

y

 µ 

∆p = 2ϕρl  4q 

(2)

( d − 2τ w )

= ∆p  π 

 ρ 

(11)

f d π d 2 

ϕ = xR y

Since e

f  

making τ w the subject from [11] above

y −5

2

d − 2τ

=2ρlx  4q 

=

2− y

 µ 

y 

(12)

∆p = 2ρl

xR y

 4q 

(3)

( w ) 

    

f ( e

d

)

π d

2 

 ∆p f

 π   ρ  

But Re =

du ρ

µ

= 4q

πµ d

=2ρlx  4q 

2τ = d −

2− y

 µ 

y −5



(13)

w   

  

Substitute for Re in [3]



− y  2

Let

 ∆p f

2− y

 π   ρ  

y

∆p = 2ρl  x  4qρ 

 =4q 

(4)

=2ρlx  4q 

 µ  

f d 

 πµd 

 π d 2 

 ∆p

 π 

 ρ 

 = Q

(14)

   

 − y  2

 f

    

∆p = 2ρlx   4qρ 

 =4q 

(5)

Tτ he=re 1f{odre− Q y −5 }

(15)

f d   πµd 

 π d 2  w 2

− y

     

4qρ

∆p = 2ρlx  

4q 1

 

(6)

3.0 MODEL VALIDATION

f  πµ d 

π d 2   d 

Since Wax thickness is a function of Friction Factor, Pressure

2 2 − y

− y − y

drop due to friction, and some rheological properties like den-

∆p = 2ρlx  4q  

1   4q 

 ρ 

 1   1  (7)

sity, viscosity and flow rate of the flowing fluid in [15]. Pres-

f  π 

 d 2   π 

 µ 

 d   d 

sure drop due to friction results shown correlation is then use

     

2 − y

   

− y − y

in [15] and a simple FORTRAN 90 program was developed to compute Wax thickness over a section of pipeline. The results

∆p = 2ρlx  4q   4q  

1   1   ρ 

 1 

(8)

obtained are presented in graphical and tubular forms to al-

f  π 

 π   d 4   d   µ 

 d 

low comparison with experimental results and other existing

         

models.

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TABLE 4.7: Variation of Wax thickness (model output) with

Reynolds number

Wax thickness output of the Model above is then compared with experimental values obtained from the work of H.S. Fogler et al. (2000), the results are presented in tabular and pictorial form as shown below.

TABLE 4.8: Comparison between Friction factor for Model output and experimental data

This is also shown graphically,

Fig.4.5: A Semi-log plot of Wax Thickness for Model results versus Reyn- olds number

Fig.4.6: A semi-log plot showing comparison between model results (output) and experimental data for wax thickness

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The wax thickness obtained from Model output above is then compared with Wax thickness obtained using other existing models under the same operating conditions, as shown below

TABLE 4.9: Comparison of Model output with other existing models (Fanning & Blasius)

Fig 4.7: A semi-log plot showing comparison of Wax thickness versus Reynolds number for model result and other existing models.

4.0 DISCUSSION OF RESULT

Wax thickness variation with Reynolds number is shown in
Table 4.7. It can be seen that when Reynolds number is 3000
Wax thickness was 0.070032mm and when Reynolds number
was 1000000, the corresponding Wax thickness was
0.005584mm. It can therefore be deduced that as Wax thick-
ness in pipeline is increasing the Reynolds number will be decreasing and vice – versa, since there will be a reduction in hydraulic diameter of the pipeline. Figure 4.5 therefore serves as a tool for predicting wax thickness in pipeline via Reynolds number.
From Table 4.8 and Figure 4.6, it can be seen that there is close agreement between model output and experimental data for wax thickness values, and there is a small or negligible devia- tion between them which confirm the accuracy of the newly developed wax model.
Also from Figure 4.7 and Table 4.9, it can be seen that there is a wide deviation between wax thicknesses measured using the other existing models and experimental value, whereas there is close agreement between model output and the experi- mental data, this further clarify the accuracy of our model.

CONCLUSION

The approach employed in this work is easily accessible since the application requires constant thermodynamic data (prop- erties that varies with temp) and rheological properties of the crude.
The following conclusion can be deduced from this research work:
An online Wax thickness measuring technique which nei- ther require depressurization and restart in order to ob- tain the measurements nor does it impose any influence on in-situ and overall heat transfer has been developed.
A tool for predicting wax thickness in pipeline via Reyn- olds number has been developed.
Wax thickness measurement model that is independent of thermodynamic data has been developed.

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