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JERT-16-1235, Liu, 1
The Experimental and Model Study on Variable
Mass Flow for Horizontal Wells with Perforated
Completion
Wei Jianguang Lin Xuesong Liu Xuemei Ma Yuanyuan
Northeast Petroleum University, Daqing City of Heilongjiang Province, 163318
Abstract:The variable mass flow in perforated horizontal wells is very complex. One reason is that the
perforation can increase the roughness of the pipe wall which will increase the frictional pressure drop. The
other is the fluid boundary layer and velocity profile of axial flow will be changed due to the “mixing” of the
inflow with the axial flow. The influences of the perforation parameters and flux rate on the pressure drawdown
in horizontal wellbore are investigated. The perforation parameters include perforation phasing, perforation
diameter, perforation density. According to the experiment results, some modes such as friction factor
calculation model (the accuracy of the model is 4%), “mixing” pressure drop calculation model (the accuracy of
the model is 3%) and total pressure drop calculation model (the accuracy of the model is 2%) are developed.
Key Words: Pressure drop Complex flow Horizontal wellbore Perforated completion
0 Introduction
The affecting rules of the pressure drop for complex flow in horizontal wells are important to the prediction
of production dynamic, the design of borehole trajectory, the optimization of completion parameters and the
inflow control method determination. The variable mass flow in perforated horizontal wellbore is complex
compared with the conventional pipe flow which embodies in two aspects. One is that the pipe wall has bigger
roughness due to the perforations which increase the frictional pressure losses. The other is that the fluid
boundary layer and velocity profile of axial flow changes due to the “mixing” of the inflow with the axial flow. A
considerable number of experimental work on pressure losses of single flow in perforated completed horizontal
wells has been published by many scholars, such as Asheim[1] and Su[2-3] of NTNU, Japanese scholar
Ihara[4-6] ,Yuan[7-10] of Tulsa, OuYang[11-13] of Stanford, Zhou Shengtian[14-15] of CUP(East China),Wang Zhiming[16-17]
of CUP(Beijing), Abdulwahid,M.A.[18]of Andhra University(India), Quan Zhang[19] of CUP (Beijing), Weipeng Jiang[20]
of Tulsa. There are three shortages of the previous work. One is the experiment systems use small size pipes
which cannot satisfy geometric similarity, kinematic similarity and dynamic similarity simultaneously which
induce the results deviated from the actual production. One is that the pipes are made of organic glass instead of
the metal and the fluid is water. The third is that the influences of the perforation phasing, perforation diameter,
perforation density on the pressure drop have not been obtained. In this paper, a full size perforated casing pipe
JERT-16-1235, Liu, 2
with 5.5 inch external diameter is used to simulate the actual production. Three values of perforation phasing,
perforation diameter and perforation density are considered respectively. The Re of axial flow is 1000-20000. The
flux ratio (the ratio of the radial volume inflow at unit wellbore length to the axial volume flow in production pipe)
is 0.01%-10%. The parameters affecting the pressure drop such as perforation phasing, perforation diameter and
perforation density, flux ratio are considered in this paper. The influence law obtained in this paper can offer a
base for development of the pressure drop model.
1 Experiment Introduction
(1) The experiment system include three units:simulation unit, fluid supply and control unit, data collection and
analyzing unit which are shown in Fig.1.
(2) The simulating unit adopts a casing with 124.0 mm inner diameter (external diameter is 5.5 inch)and a casing
pipe with 149.1 mm inner diameter(external diameter is 7.5 inch). This unit is 6.5m long and the distance
between two pressure monitoring nodes is 6 m. To improve the accuracy of the pressure difference transmitter,
the pressure monitoring nodes are connected with difference pressure transmitter by softy sheer plastic pipes.
The accuracy of the pressure difference transmitter is the order of magnitude of 1Pa. The outside wall of the
inner pipe is covered by compact gauze. At the ends of this unit, there are two liquid inlets to ensure the inflow
profile uniform. The simulating unit is shown in Fig.2.
(3) The mineral oil of 10 mPa.s is used instead of crude oil. Before every experiment, the indoor temperature and
viscosity of the mineral oil is measured to make sure the temperature and viscosity in each experiment is same.
(4) Three values of screw perforating phasing in simulation unit are considered: 45°,90°,180°,as shown in
Fig.3. The values of perforation density are 8 meter-1, 16 meter-1, 24 meter-1. The values of perforation diameter
are 10mm, 20mm, 30mm.
(5) The Re of axial flow is 1000-20000. The flux ratio is 0.01%-10%.
JERT-16-1235, Liu, 3
Fig 1 Experiment System for Complex Flow in Horizontal Wellbore
Fig 2 Simulation Unit Diagram
Fig 3A 45°Screw Perforating Phasing
A
A
B
B
C
C
D
D
E
E
F
F
G
G
H
H
A B C D
E F G H
JERT-16-1235, Liu, 4
Fig 3B 90°Screw Perforating Phasing
Fig 3C 180°Screw Perforating Phasing
2 Experiment Results
It is need to emphasize that the inner diameter of these experimental pipes are all 124 mm, the distance of
two pressure measurement nodes is 6m,and the ordinary casing pipe is the casing without perforation. The
relationship curves of Re of axial flow with frictional pressure drop gradient under different perforation density,
diameter, phasing without inflow are shown in fig.4A, fig.4B, fig.4C respectively. From fig.4A, fig.4B, fig.4C, the
effects of perforation density, diameter, phasing on frictional pressure losses are significant. The frictional
pressure losses always increase with the increase of perforation density, diameter and phasing. When the
perforation diameter is 20mm, the perforation phasing is 90°, the Re of axial flow is 20000,the frictional
pressure drop gradient is 376 Pa/m,414 Pa/m,459 Pa/m which is bigger than that of the ordinary casing pipe by
11.11%,22.41%,35.71% corresponding to the perforation density of 8 m-1,16 m-1,24 m-1 respectively. When the
perforation density is 16 m-1,the perforation phasing is 90°,the Re of axial flow is 20000,the frictional pressure
drop gradient is 389Pa/m,414Pa/m,441Pa/m which is bigger than that of the ordinary casing pipe by
15.14%,22.41%,30.46% corresponding to the perforation diameter of 10 mm,20 mm,30 mm respectively. When
the perforation density is 16 m-1,the perforation diameter is 20 mm, the Re of axial flow is 20000,the frictional
pressure drop gradient is 399Pa/m、414Pa/m、430Pa/m which is bigger than that of the ordinary casing pipe by
A
A
B
B
C
C
D
D
A B C D
A
A
A B
B
B
JERT-16-1235, Liu, 5
17.96%,22.41%,27.14% according to the perforation phasing of 45°, 90°, 180°respectively. The results
indicate that the perforation can increase the roughness of the pipe wall which increases the frictional pressure
drop.
To analyze the influence of flux ratio on total and “mixing” pressure drop, the relation curves of total
pressure drop with the flux ratio under different perforation density, diameter, phasing when the Re at outlet
keeps 5000 are obtained in fig.5A, fig.5B and fig.5C, and the relationship curves when the Re of outlet keeps
5000 are obtained in fig.6A, fig.6B and fig.6C. From the fig.5A, fig.5B and fig.5C, we can see that the effect of flux
ratio on total pressure drop is significant. The total pressure drop increases with the flux ratio. The pressure drop
gradient is 28Pa/m、36 Pa/m,45 Pa/m,82 Pa/m which is bigger than the frictional pressure drop of the ordinary
casing pipe(about 29 Pa/m) by -3%,25%,56% ,185% when the flux ratio is 0.01%,0.1%,1%,10% respectively, that
indicates that when the flux ratio is small, the inflow can reduce the frictional pressure drop compared with the
ordinary casing pipe without perforations while the high flux ratio can increase the “mixing” and acceleration
pressure drawdown obviously. The effect of flux ratio is greater than the effect of perforation parameters. From
the fig.6A, fig.6B, fig.6C, the “mixing” pressure drop increases with the flux ratio, but there exists a critical value
of flux ratio. When the actual flux ratio less than the critical value, the “mixing” pressure drop is negative which
means that the inflow fluid can reduce the total pressure drop. When the actual flux ratio bigger than the critical
value, the “mixing” pressure drop is positive and could increases the total pressure drop. The critical flux ratio
increases with the perforation density and perforation diameter. In this paper, the critical value is 0.05%-0.1%.
Fig.7A and fig.7B present the relation curves of the flux ratio with the pressure drop gradient when the Re at
outlet is 5000 and 15000 respectively. From fig.7A and fig.7B, no matter the value of the Re, if the flux ratio is
less than 0.1% the acceleration pressure drop can be neglected. If the flux ratio is greater than 0.1% the
acceleration pressure drop increases significantly with the flux ratio. The Re of axial flow can also affect
acceleration pressure drop. When the Re of axial flow is 5000, the frictional pressure drop gradient is 36 Pa/m,
the acceleration pressure drop is 0.36 Pa/m, 3.6 Pa/m, 34 Pa/m corresponding to the 0.1%, 1%, 10% flux ratio
where the acceleration pressure drop of 10% flux ratio is almost same with frictional pressure drop. When the Re
of axial flow is 15000 and the frictional pressure drop gradient is 242 Pa/m, the acceleration pressure drop is 3.26
Pa/m, 32 Pa/m, 309 Pa/m corresponding to the 0.1%, 1%, 10% flux ratio where the acceleration pressure drop at
10% flux ratio is more than frictional pressure drop.
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Fig 4A Frictional Pressure Drop Gradient versus Re with Different Perforation Density without Inflow
Fig 4B Frictional Pressure Drop Gradient versus Re with Different Perforation Diameter without Inflow
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Fig 4C Frictional Pressure Drop Gradient versus Re with Different Perforation Phasing without Inflow
Fig 5A Total Pressure Drop Gradient versus Flux Ratio with different perforation density with Inflow
Fig 5B Total Pressure Drop Gradient versus Flux ratio with different perforation diameter with Inflow
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Fig 5C Total Pressure Drop Gradient versus Flux Ratio with different perforation phasing with Inflow
Fig 6A “mixing” Pressure Drop Gradient versus Flux ratio with different perforation density with Inflow
JERT-16-1235, Liu, 9
Fig 6B “mixing” Pressure Drop Gradient versus Flux Ratio with different perforation diameter with Inflow
Fig 6C “mixing” Pressure Drop Gradient versus Flux ratio with different perforation phasing with Inflow
Fig 7A The Pressure Drop Gradient versus Flux ratio with Re=5000 of Axial Flow
JERT-16-1235, Liu, 10
Fig 7B The Pressure Drop Gradient versus Flux ratio with Re=15000 of Axial Flow
3 Models
The total pressure drop(the sum of frictional pressure drop, “mixing” pressure drop, acceleration pressure
drop) in horizontal wellbore includes frictional pressure drop, “mixing” pressure drop, acceleration pressure drop
[21]:
w a m tp p p p (1)
The frictional pressure drop is Darcy–Weisbach[22] equation:
2
w w2
L Vp f
D
(2)
The friction factor [3] of perforated wall is
*
w w
8 Re 82.5ln 3.75
2
uB
f f u
(3)
in which B is a function of frictional coefficient 0f of ordinary pipe:
0 0
8 Re 82.5ln 3.75
2B
f f
(4)
and the 0f can be calculated by the Haaland equation[23] given by
1.11
0
1 6.91.8log
Re 3.7
D
f
(5)
The roughness function */u u ( the function of perforation diameter, perforation density and wellbore
JERT-16-1235, Liu, 11
diameter) can be calculated from the empirical correlation[24]:
p p
1*
2
AA
d nu
u D
(6)
From the experiment results, the values of1 2,A A under different perforation parameters are given in table 1.
The fig.8 presents the accuracy of the frictional pressure drop model. From the fig.8 we can see that the relative
error of the model is less than 3%.
Fig.8 Precision Verification of Frictional Pressure Drop Calculation Model
According to the relation curves of the flux ratio with the “mixing” pressure drop(The pressure drop caused
by heat loss and disturbance after the wall entering current and shaft main current’s mixing), the “mixing”
pressure drop is in a linear relationship with flux ratio,so the function is given by
m 1 w 2B lg Bp R (7)
in which the 1 2,B B is given in table 1. The fig.9 presents the accuracy of the “mixing” pressure drop model.
From the fig.9 we can see that the relative error of the model is less than 5%.
JERT-16-1235, Liu, 12
Fig.9A Precision Verification of “mixing” Pressure Drop Calculation Model with Re=5000 in Axial Flow
Fig.9B Precision Verification of “mixing” Pressure Drop Calculation Model with Re=15000 of Axial Flow
Based on the principle of momentum conservation, the acceleration pressure drop is calculated by Eqs.8
2 2
a 2 1p V V (8)
The fig.10 presents the accuracy of the total pressure drop model. From the fig.10 we can see that the
relative error of the model is less than 4%.
+5%
-5%
JERT-16-1235, Liu, 13
Fig.10A Precision Verification of Total Pressure Drop Calculation Model with Re=5000 of Axial Flow
Fig.10B Precision Verification of Total Pressure Drop Calculation Model with Re=15000 of Axial Flow
Tab.1 The Coefficient of Models
Perforation
Density
(shot/m)
Perforation
Diameter
(mm)
Perforation
Phasing
(°)
A1 A2 B1 B2
8 20 90 6.21 12.4
6.66
9.28
16 20 90 8.00 16.0 7.30
24 20 90 9.30 18.6 6.15
16 10 90 5.82 16.0 8.37
16 30 90 9.14 16.0 6.53
16 20 45 6.52 16.0 7.89
16 20 180 9.51 16.0 6.81
+4%
-4%
+4%
-4%
JERT-16-1235, Liu, 14
4 Conclusions
(1) Perforations can increase the roughness of the pipe wall obviously which lead to the additional frictional
pressure drop. The frictional pressure drop increases with the perforation density, diameter, phasing. In this
paper, the perforation density varies 8-24 shots per meter, the perforation diameter is 10-30 mm, the perforation
phasing is 45-180 degree, and the frictional pressure drop is greater than that of ordinary pipe by 11%-35%.
(2) The effect of flux ratio on total pressure drop is significant .The total pressure drop increases with the flux
ratio. The pressure drop gradient is bigger than the frictional pressure drop of the ordinary casing pipe(about 29
Pa/m) by -3%,25%,56% ,185% when the flux ratio is 0.01%,0.1%,1%,10% respectively.
(3) There is a critical value of flux ratio(in this paper, it is 0.05%-0.1%)for the “mixing” pressure drop. When the
actual flux ratio is less than the critical value, the “mixing” pressure drop is negative. When the actual flux ratio is
bigger than the critical value, the “mixing” pressure drop will increase to a positive value. The scale of the flux
ratio increases with the perforation density and perforation diameter.
(4) When the flux ratio is less than 0.1%, the proportion of acceleration pressure drop can be neglected. When
the flux ratio greater than 0.1%, the frictional pressure drop increases with the flux ratio obviously. When the Re
of axial flow is 5000, the acceleration pressure drop is same with the frictional pressure drop under the 10% flux
ratio. When the Re of axial flow is 15000, the acceleration pressure drop is bigger than the frictional pressure
drop by 10% under the 10% flux ratio.
(5) With the increase of flux ratio, the proportion of frictional pressure drop reduces. When the flux ratio is less
than 0.1%, the proportion of frictional pressure drop is 97%.When the flux ratio increases to 1%, the proportion
of frictional pressure drop reduces to 75%.When the flux ration is 10%, the proportion of frictional pressure drop
is as low as 40%.
(6) With the increase of flux ratio, the proportion of acceleration pressure drop increases. When the flux ratio is
less than 0.1%, the proportion of acceleration pressure drop can be neglected. When the flux ratio increases to
1%, the proportion of acceleration pressure drop is about 10%. When the flux ration is 10%, the proportion of
acceleration pressure drop can increase to 45%.
(7) When the flux ratio is less than 1%, the “mixing” pressure drop increases with the flux ratio. When the flux
ratio is bigger than 1%, the proportion of “mixing” pressure drop is always nearly 15%.
(8) The relative error of the results of frictional pressure drop model, “mixing” pressure drop model and the total
JERT-16-1235, Liu, 15
pressure drop model with the experiment results are less than 3%, 5%, 4% respectively.
Nomenclature
tp —total pressure drop in perforated horizontal wellbore, Pa
wp —frictional pressure drop in perforated horizontal wellbore, Pa
ap —acceleration pressure drop in perforated horizontal wellbore, Pa
mp —“mixing” pressure drop in perforated horizontal wellbore, Pa
wf —friction coefficient of the wall in perforation well, dimensionless
L —wellbore length, m
D —wellbore diameter of the perforation well, m
—density of the fluid, kg/m3
V —velocity of axial flow in wellbore, m/s
1V —velocity at inlet of wellbore, m/s
2V —velocity at outlet of wellbore, m/s
Re —Reynolds number of axial flow, dimensionless
pd —perforation diameter, m
pn —perforation density, shot per meter
of —frictional factor of ordinary pipe, dimensionless
—absolute roughness of pipe wall, m
wR —the average-velocity ratio between the wall inflow and wellbore section current, dimensionless
References
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Journal,1998,3(2):124~133.
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Horizontal Wellbore[J]. Journal of Energy Resources Technology,2014,136(4):1~7.
[19] Quan Zhang, Zhiming Wang, Xiaoqiu Wang, Jiankang Yang. A New Comprehensive Model for Predicting the Pressure Drop of
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JERT-16-1235, Liu, 17
[21] Wang Z M, The Optimization Theory and Application of Well Completion for Complex Structure Wells[M], Petroleum Industry
Press,2010,55~57.
[22] White, F.M., Fluid Mechanics, McGraw-Hill, Inc., 1986.
[23] Ito,H. and Imai, K., “Energy Losses at 90°Pipe Junctions”, Journal of the Hydraulics Division, Proc. ASCE, September,
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[24] Gardel, A., “Les Pertes de Charge Dans Les Ecoulements au Travers de Branchements En Te”, Lausanne Univ. Polytech. Ecole
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Author:. Author introduction: Wei Jianguang, male, associate professor. Research area:
theory and technique of well completion optimization, theory and technique of EOR,
seepage mechanism of unconventional oil and gas. Tel:13634663105, E-mail:
weijianguang@163.com.
Natural Science Foundation of Heilongjiang Province project” research on the change
pattern of working viscosity of polymer solution in the reservoir” (No.D2015008)
Natural Science Foundation of China project” research on seepage mechanism of
gas-water two phase in the shale gas reservoir considering the condition of pollution”
(No.51474070)
Figure captions
Fig 1 Experiment System for Complex Flow in Horizontal Wellbore
Fig 2 Simulation Unit Diagram
Fig 3A 45°Screw Perforating Phasing
Fig 3B 90°Screw Perforating Phasing
Fig 3C 180°Screw Perforating Phasing
Fig 4A Frictional Pressure Drop Gradient versus Re with Different Perforation Density without Inflow
Fig 4B Frictional Pressure Drop Gradient versus Re with Different Perforation Diameter without Inflow
Fig 4C Frictional Pressure Drop Gradient versus Re with Different Perforation Phasing without Inflow
Fig 5A Total Pressure Drop Gradient versus Flux Ratio with different perforation density with Inflow
Fig 5B Total Pressure Drop Gradient versus Flux ratio with different perforation diameter with Inflow
Fig 5C Total Pressure Drop Gradient versus Flux Ratio with different perforation phasing with Inflow
Fig 6A “mixing” Pressure Drop Gradient versus Flux ratio with different perforation density with Inflow
Fig 6B “mixing” Pressure Drop Gradient versus Flux Ratio with different perforation diameter with Inflow
Fig 6C “mixing” Pressure Drop Gradient versus Flux ratio with different perforation phasing with Inflow
Fig 7A The Pressure Drop Gradient versus Flux ratio with Re=5000 of Axial Flow
JERT-16-1235, Liu, 18
Fig 7B The Pressure Drop Gradient versus Flux ratio with Re=15000 of Axial Flow
Fig.8 Precision Verification of Frictional Pressure Drop Calculation Model
Fig.9A Precision Verification of “mixing” Pressure Drop Calculation Model with Re=5000 in Axial Flow
Fig.9B Precision Verification of “mixing” Pressure Drop Calculation Model with Re=15000 of Axial Flow
Fig.10A Precision Verification of Total Pressure Drop Calculation Model with Re=5000 of Axial Flow
Fig.10B Precision Verification of Total Pressure Drop Calculation Model with Re=15000 of Axial Flow
Table captions
Tab.1 The Coefficient of Models
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