Predicting downhole natural separation efficiency by a ... - SciELO

Rev. Téc. Ing. Univ. Zulia. Vol. 30, Edición Especial, 336 - 343, 2007 

Predicting downhole natural separation efficiency 

by a correlation 

Richard Márquez and Mauricio Prado 

The University of Tulsa. Arizona, USA. rmarquez@luz.edu.ve; Mauricio-prado@utulsa.edu 

Phone: 0414-6137946 (Vzla); 001-918-6315163 (USA). 

Abstract 

Quantifying the downhole natural separation efficiency will help to minimize the presence of free gas 

at pump intake and to avoid certain operational problems, such as: gas lock, surging, cavitation, over 

heat, among others, in systems of artificial lift by pumps. In the last few years, the University of Tulsa Artificial 

Lift Projects (TUALP) experimental facilities were used to obtain important experimental data on natural 

separation. This data has allowed the development of simplified models such as Alhanati [1] and 

Serrano [9]. Even though previous models have been able to estimate the natural separation efficiency, 

both models never considered the effect of important variables as the slip velocity in the radial direction 

and the geometric characteristic of the bottomhole completion. This paper presents a new correlation obtained 

from TUALP experimental data. This work is different than previous simplified models since it considers 

the drag effect in the radial direction. This new model represents a simple and reliable tool, which 

allows a robust estimate of the natural separation efficiency with a higher accuracy. 

Key words: Natural separation, free gas, slip velocity, artificial lift. 

Predicción de la eficiencia de separación natural 

en fondo de pozo mediante una correlación 

Resumen 

Cuantificar la eficiencia de separación natural en el fondo del pozo permitiría minimizar la presencia 

de gas libre a la entrada de la bomba y evitar ciertos problemas operacionales, tales como: fluctuaciones 

de producción, cavitación, sobre calentamiento, entre otros, en sistemas de levantamiento artificial mediante 

bombas. En los últimos años, las facilidades experimentales del proyecto de levantamiento artificial 

de la Universidad de Tulsa (TUALP) han sido utilizadas para obtener importante data experimental sobre 

separación natural. Esta data ha permitido el desarrollo de modelos simplificados como de Alhanati 

[1] y Serrano [9]. Aun cuando estos modelos han permitido estimar la eficiencia de separación natural, 

ambos modelos nunca han considerado el efecto de importantes variables como la velocidad de deslizamiento 

en la dirección radial y las características geométricas de la completación del pozo. Este artículo 

presenta una nueva correlación obtenida de data del TUALP. Este trabajo es diferente de anteriores modelos 

simplificados ya que considera el efecto de arrastre en la dirección radial. Este nuevo modelo representa 

una simple y confiable herramienta, la cual permite estimar la eficiencia de separación natural con un 

alto grado de exactitud. 

Palabras clave: Separación natural, gas libre, velocidad de deslizamiento, levantamiento artificial. 

Rev. Téc. Ing. Univ. Zulia. Vol. 30, Edición Especial, 2007

Predicting downhole natural separation efficiency by a correlation 337 

I. Introduction 

Since 1993, Tulsa University Artificial Lift 

Projects (TUALP) has been conducting important 

research in the area of natural separation. It has 

permitted gathering experimental data, using air 

and water, to develop, test, validate, and improve 

different correlations and models for estimating 

natural separation efficiency. Based on the 

drift-flux model and assuming no slip velocity in 

the radial direction, in front of the pump intake, 

some simplified models have been developed at 

TUALP, such as: Alhanati’s [1] and Serrano’s [9] 

models. Although these models have captured 

the physics involved in the problem, results have 

shown that they do not work very well for all operational 

conditions. On the other hand, simplified 

models do not consider the effect of important 

variables, such as: gas flow rate, pressure, geometric 

characteristics of the bottomhole and drag 

force in the radial direction, which have shown to 

have a strong effect on the natural separation 

process. A new assumption (the existence of the 

slip velocity in the radial direction) has allowed 

obtaining a new mathematical formulation for 

the problem. Available experimental data was 

used to develop a new correlation. Results obtained 

for the new simplified model show the 

strong effect that the drag force has on the separation 

process. The new simplified model, with 

along the new correlation, represent an important 

change in the methodology used to predict 

natural separation efficiency. 

II. General Formulation 

of the New Simplified Model 

A single control volume situated in front of 

the pump intake is showed in Figure 1. Three assumptions 

will be considered valid. The first 

states that: the gas void fraction g is considered 

uniform across to the annulus domain and holds 

constant up to the pump intake port. The second 

considers that the liquid column in the annulus 

in front and above the pump intake is not flowing 

in the vertical direction; it flows only in a radial 

direction towards the pump intake. The third 

considers the existence of slip velocity between 

gas and liquid phases at the vertical and radial 

direction. 

Casing Wall 

Assuming constant density, mass balance 

equation would allow establishing the following 

volumetric balance around the single control volume 

(as shown in Figure 2): 

Q 

i 

l 

i 

p 

l 

Q , (1) 

p 

Qg 

Qg 

Qgp, (2) 

i 

where Q l 

and Q p 

l 

represent the liquid flow rate 

coming from the annulus and liquid flow rate going 

inside the pump, respectively. Similarly, Q i g , 

Q p 

gp 

and Q g are the gas flow rate coming from the 

annulus, gas flow rate going into the pump and 

the gas flow rate vented, respectively. On the 

other hand, natural separation efficiency is defined 

as the ratio of the gas flow rate vented to the 

gas flow rate coming from the annulus, i.e., 

Q g 

E i 

. (3) 

Q 

g 

Gas flow rate can also be expressed as a 

function of superficial velocity and flow area, i.e., 

p 

p 

Qgp 

VrsgA 

i i 

Q V A 

g 

zsg 

where V p 

rsg 

p 

Ann 

Annulus Outlet 

g 

A Ann 

Annulus Inlet 

, (4) 

i 

and V zsg 

A p 

Pump Wall 

Shaft 

Pump Intake 

represent the superficial gas 

velocity going into the pump and the superficial 

gas velocity coming from the annulus, respectively. 

A p and A Ann 

are the area of the port and the 

r 

Figure 1. Single Cell Domain. 

Z 


338 Márquez and Prado 

annulus, respectively. Combining Eqs. 1 to 4, 

natural separation efficiency would be given by: 

p 

V A 

rsg p 

E 1 

i . (5) 

V A 

zsg 

Ann 

Q gv 

r 

Z 

Based on a single control volume, as shown 

in Figure 3, the following velocities field for gas 

and liquid phases, respectively, would be assumed 

valid in this work. 

g 

p 

Q l 

p 

Q gp 

V V ; V V 

, (6) 

zg 

i 

zg 

rg 

p 

rg 

p 

zl rl rl 

V 0 ; V V 

. (7) 

i 

Q g 

i 

Q l 

The slip velocity V s is defined as: 

Figure 2. Flow Rates Distribution around 

the Control Volume. 

Vs Vg Vl 

, (8) 

Z 

where V g and V l 

represent the average actual gas 

r 

and liquid velocity, respectively. In the radial direction, 

the slip velocity definition given by Eq. 8, 

allows to obtain the following equation: 

V __ 

rl 

V __ 

zg 

V __ 

g 

rg 

p 

V 

p p rsg Vrsl 

Vrs Vrg Vrl Vrg 

Vrl 

, (9) 

( 1 ) 

p 

g 

g 

V __ 

rg 

where V p rg and V p rl 

represent the actual gas and 

liquid velocity, respectively, going into the pump. 

Combining Eqs. 1 and 9, the following equation 

for V p 

rsg can be written as: 

Liquid Phase Flow 

Gas Phase Flow 

Figure 3. Velocities Field into the Control 

Volume. Gas and Liquid Phase Flow. 

 

A 

V 

p 

g 

i Ann 

Vrsg 

Vrs g V 

rs and V zs , respectively. Using the drift-flux 

( 1 ) 

zsl 

g 

A 

. (10) 

1 

model approach proposed by Ishii [5], the slip velocity 

V s at any direction can be related to the ter- 

 

p 

 

minal velocity of a particleV . This relationship is 

At the vertical direction, the slip velocity given by: 

definition given by Eq. 9 and the assumptions 

considered previously can be used to obtain the 

n1 

Vs 

V( 1 g) 

. (12) 

following equation: 

i 

n represents the effect due to the presence 

V 

i zsg 

Vzs 

Vzg 

. (11) of others bubbles and may be negligible under 

g 

churn flow regime. Since most of the available experimental 

data is mainly under this flow regime, 

The solution of Eqs. 10 and 11 depends on then n will be assumed equal to zero. Therefore, 

two additional unknown variables, i.e. the slip Eq. 12 allows rewrite Eqs. 10 and 11 as a function 

of the terminal velocity (V z and V r 

velocity in the radial and vertical direction, V rs ). 



 

p 

g 

i 

Vrsg 

Vr 

V 

 

 

1 g 

 

i 

zsl 

 

A 

 

A 

Ann 

p 

 

 

, (13) 

 

 

g 

Vzsg 

1 

. (14) 

g V 

z 

Combining Eqs. 13 and 14 and replacing 

into Eq. 5, natural separation efficiency would be 

finally given by: 

Velocity at vertical direction V z can be determined 

by using the Ishii’s model. According to 

Ishii [6], V z for bubbly and slug/churn flow regime 

is given by: 

V 

z 

( 

l 

g 

) g 

 

 

 

2 

2 

l 

1/ 

4 

. (16) 

Therefore, the only unknown variable is the 

parameter called X, defined from Eq. 15 as: 

V A 

i 

r p Vzsl 

E 

 

 

 

1 

 

. (15) 

 

V 

A V 

z 

Ann 

z 

X 

V 

 

V 

r 

z 

A 

 

 

 

 

A 

p 

Ann 

 

E 

V i 

 

 

zsl 

1 

. (17) 

V 

z 

Eq. 15 depends on superficial liquid velocity 

V zsl 

i 

, geometric configuration of the bottomhole 

Ap 

/ AAnn, and the terminal velocity ratio 

Vr 

/ Vz. Terminal velocity at vertical direction 

V z can be estimated from models such as 

Harmathy [3], Wallis [10], Ishii and Zuber [6], 

among others. The geometric characteristics of 

the bottomhole can also be easily determined. 

The problem is how to estimate the terminal velocity 

in the radial direction V r . In this paper, a 

correlation will be showed as a solution for V r . 

III. New Correlation 

According to Eq. 15, natural separation efficiency 

E and superficial liquid velocity coming 

i 

from the annulus V zsl 

are two known variables, 

because experimental data, gathered at TUALP 

since 1993, is available for this work. Terminal 

The available experimental data for natural 

separation efficiency allowed plotting a graph of 

i 

X vs. Vzsl 

/ Vz , as shown in Figure 4. According 

to Figure 4, for low liquid flow rates the slip effect 

in the radial direction can be negligible. Therefore, 

the assumption of no slip velocity in the radial 

direction, considered by Alhanati, would result 

valid. However, for higher liquid flow rates 

this assumption cannot be considered anymore. 

Serrano corroborated this fact later when extended 

Alhanati’s model by gathering extra experimental 

data for higher liquid and gas flow 

rates. Alhanati’s model failed to match the data 

taken by Serrano. Consequently, Serrano tried 

to obtain a better model by developing an empirical 

correlation to predicting the local gas void 

fraction for the region in front of the pump inlet 

ports, assuming no slip velocity in the radial direction. 

2 

0 

0 1 2 3 4 5 6 7 8 9 10 

-2 

X Parameter 

-4 

-6 

-8 

-10 

V zsl/V zoo 

EXP. DATA - ALHANATI EXP. DATA - SAMBANGI EXP. DATA - SERRANO 

Figure 4. X Parameter. 



The new model proposed assumes the existence 

of the slip velocity in the radial direction 

and its effect could be considered by developing a 

correlation from Figure 4. Using a nonlinear regression 

model, the following correlation for X parameter 

was found. 

 

 

ab c 

 

V V 

X 11 

 

i 

V 

b 

 

 

Vz 

i 

zsl 

z 

d 

zsl 

 

d 

 

 

 

 

 

 

 

 

 

272 

V 

 

V 

i 

zsl 

z 

 

 

272 

1/ 272 

 

 

 

 

 

 

 

, 

(18) 

where the coefficients a,b,c and d are given by: 

Finally, natural separation efficiency may 

be calculated by: 

 

ab c V i 

d 

 

zsl 

 

 

 

 

Vz 

 

E 

 

 

 

1 

 

i 

d 

Vzsl 

b 

 

 

 

 

 

 

V 

 

 

z 

 

. 

272 

V 

 

V 

i 

zsl 

z 

 

 

272 

1/ 

272 

 

 

 

 

 

 

 

V 

 

V 

i 

zsl 

z 

(19) 

A graph of New Model Predicted Efficiency 

vs. Measured Efficiency from TUALP data bank is 

shown in Figure 5. 

IV. Results and Discussions 

Model Comparisons 

 

 

 

The evaluation of this study was based on 

statistical parameters given by average percentage 

error E1, absolute average percentage error 

E2 and the standard deviation E3. 

N 

1 

E1 

 

e N ri 100, (20) 

 

i1 

N 

1 

E2 

 

e N ri 100, (21) 

 

E3 

 

i1 

N 

2 

1 E1 

 

eri 

 

100 

N 1i 

1 

100 

, (22) 

 

 

where N represents the number of data points. 

On the other hand, the error e ri is given by: 

e 

ri 

E 

 

E 

E 

cal , i meas, 

i 

meas, 

i 

. (23) 

The performance of the new simplified 

model proposed in this paper was compared with 

others simplified models, such as: Alhanati and 

Serrano. Results have been divided in two categories, 

as follow: For low gas void fraction, it was 

found a 14.41% of average error in the prediction 

of natural separation by using the new correlation. 

For high gas void fraction, the error is much 

lower compared with the others simplified models. 

The overall performance of Alhanati’s model 

represents a 25.64% against of 17.43% of the 

new simplified model proposed. 

Drag Effect 

1.00 

0.90 

0.80 

Predicted Efficiency 

0.70 

0.60 

0.50 

0.40 

0.30 

0.20 

0.10 

0.00 

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 

Measured Efficiency 

EXP. DATA - ALHANATI EXP. DATA - SAMBANGI EXP. DATA - SERRANO 

Figure 5. Predicted vs. Measured Natural Separation Efficiency. New Correlation. 



According to Figure 4, the slip in the radial 

direction can be negligible for low liquid flow 

rates. However, this assumption cannot be considered 

anymore for high liquid flow rates. The 

new correlation takes in account that effect, so 

predictions on natural separation will able to be 

estimated with higher accuracy, as a shown in 

Figure 5. 

Effect of Viscosity 

Unfortunately, the model proposed for V z 

does not allow considering the bubble size and 

viscosity effect. However, other formulations for 

C d 

would be able to be used instead of recommended 

by Harmathy [3]. For example, if the following 

correlation is considered forC d 

(Stoke flow 

condition), 

C d 

24 

Re , (24) 

p 

where, the particle Reynolds number Re p is defined 

as: 

2r V 

 

. (25) 

d s l 

Re p 

l 

The terminal velocity in the vertical direction 

V z would be given by: 

V 

z 

2 

de 

l 

2 r 

9 

( ) g. (26) 

l 

g 

As a consequence, the Eq. 26 would be able 

to be used in order to consider the viscosity and 

the bubble size effect in the prediction of natural 

separation efficiency. However, one additional 

closure relationship for the drag radius r d 

would 

be required in this case. 

Effect of Geometry 

The model was used to predict natural separation 

efficiency for a 4 in. pump diameter inside 

5, 7 and 10 in. casings. According to 

Figure 6, natural separation efficiency increases 

as the annulus area increases. 

Effect of Gas 

Lea and Bearden [7] conducted tests with 

500 series equipment inside a 7” casing, with air 

and water as experimental fluids at low pressures 

(25 to 30 Psig). According to their results, 

natural separation efficiency increases as the 

in-situ-free gas increases. Alhanati and 

Sambangi also reported the same observation. 

Unfortunately, the new correlation is not sensible 

to the gas flow rate. It does not appear to have any 

effect in the prediction of natural separation. 

Effect of Pressure 

Experiments have captured the effect of 

that variable in the separation process. However, 

the new simplified model, with along the new correlation, 

does not incorporate the effect of that 

variable in the prediction of natural separation. 

The only possible effect is through the fluid physical 

property calculation given by Eq. 16. The new 

Efficiency 

1.0 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0.0 

0 500 1000 1500 2000 2500 3000 3500 4000 4500 

Liquid Flow Rate (BPD) 

Dc=5in Dc=7in Dc=10in 

Dp = 4 in 

Figure 6. Effect of Geometry on Natural Separation Efficiency. 



simplified model developed should be improved 

to better incorporate the pressure effects observed 

in the experimental data. 

V. Conclusions and 

Recommendations 

This new model considers the effect of slip 

velocity in the radial direction, a variable neglected 

in previous simplified models. In addition, 

this variable is considered through a new 

and reliable correlation obtained from available 

experimental data at TUALP. 

Results obtained in this work show the 

strong effect that slip velocity has in the prediction 

of natural separation efficiency, not only in 

the vertical direction, but also in the radial direction, 

especially for high liquid flow rates. 

The new model presented in this work need 

to be improved. Variables such as gas void fraction 

and gas flow rate must be considered in the 

prediction of natural separation, because experimental 

results have shown have theirs effect on 

the separation process. 

Additional real experimental data is required 

to further verify the results obtained by 

using this new correlation. In addition, the viscosity 

effect could be considered and analyzed. 

A = 

D = 

E = 

Q = 

V = 

Area, in. 

Subscripts 

VI. Nomenclature 

Diameter, in. 

Natural Separation Efficiency 

Flow Rate, BD 

Velocity, ft/sec 

Ann= Annulus 

c = Casing 

g = Gas 

i = Inlet 

l = Liquid 

p = Port, Pump 

t = Tubing 

s = Slip, Superficial 

r, z = Direction 

VII. Acknowledgements 

Authors wish to thank Eni-Agip, Centrilift, 

Pemex, Pdvsa-Intevep, Ongc, Schlumberger, 

Shell and Totalfinalelf for supporting this study. 

References 

1. Alhanati, F.J.S.: “Bottomhole Gas Separation 

Efficiency in Electrical Submersible 

Pump Installation”, Dissertation. The University 

of Tulsa, 1993. 

2. Ghauri, W.K.: “Production Technology Experience 

in a Large Carbonate Water-Flood, 

Denver Unit, Wasson San Andres Field, West 

Texas”, paper SPE 8406 presented at the 

1979 SPE Annual Technical Conference and 

Exhibition, Las Vegas, NV, Sep. 23-26. 

3. Harmathy, T.Z.: Velocity of Large Drops and 

Bubbles in Media of Infinite or Restricted Extent, 

AIChE, 6, 281(1960). 

4. Harun, A.F., Prado, M.G., Serrano, J.C. and 

Doty, D.R.: “A Simple Model to Predict Natural 

Gas Separation Efficiency in Pumped 

Wells”, paper SPE 63045 presented at the 

2000 SPE Annual Technical Conference and 

Exhibition held in Dallas, Texas, 1-4 October 

2000. 

5. Ishii, M.: “Thermo Fluid Dynamic Theory of 

Two Phase Flow”, Eyrolles, Paris, 1975. 

6. Ishii, M. and Zuber, N.: “Drag Coefficient and 

Relative Velocity in Bubbly, Droplet or Particulate 

Fluids”, AIChE Journal (September 

1979) 25, No. 5, 843-855. 

7. Lea, J.F. “Effect of Gaseous Fluids on Submersible 

Pump Performance”, paper SPE 

9218 presented at the 1980 SPE Annual 

Technique Conference and Exhibition, Dallas, 

TX. (Sep. 21-24). 

8. Marquez, R., “Classification of the experimental 

natural separation data according to 

flow pattern regime”. Technical Report. The 

University of Tulsa, Tulsa, Ok. (2002). 

9. Serrano, J.C.: “Natural Separa Ishii, M.: 

“Thermo Fluid Dynamic Theory of Two Phase 

Flow”, Eyrolles, Paris, 1975.tion Efficiency in 

Electric Submersible Pump Systems”, Dissertation. 

The University of Tulsa, 1999. 



10. Wallis, G.B.: “The Terminal Speed of Single 

Drops or Bubbles in an Infinite Medium”, International 

Journal of Multiphase Flow 

(1974) 1, 491-511. 

11. Zuber, N.: “On the Dispersed Two-Phase 

Flow in the Laminar Flow Regime”, Chem. 

Eng. Sci., 19, 897 (1964). 

Recibido el 30 de Junio de 2006 

En forma revisada el 30 de Julio de 2007

Predicting downhole natural separation efficiency by a ... - SciELO

Create successful ePaper yourself

Delete template?

Save as template?