experimental study of a multistage helico-axial gas
TRANSCRIPT
IV Journeys in Multiphase Flows (JEM 2015) March 23-27, 2015, Campinas, SP, Brazil
Copyright Β© 2015 by ABCM Paper ID: JEM-2015-XXXX
EXPERIMENTAL STUDY OF A MULTISTAGE HELICO-AXIAL GAS
HANDLER OPERATING WITH WATER AND AIR
CΓ©sar Longhi Petrobras β International Technical Support β Rua do Senado, 20031 β 12th Floor β Rio de Janeiro β RJ β B razil
Unicamp β Mechanical Engineering β Energy Department β Rua Mendeleyev, 200 β Campinas β SP β Brazil
Abstract. Electrical Submersible Pumps are multistage devices employed in the petroleum industry to produce oil.
The ESP geometry was originally designed to operate with low viscosity liquids. The presence of a secondary gaseous
phase reduces the developed pressure and causes the surging phenomenon, characterized by the system instability.
Gas handlers are rotary devices with special geometries which degrade less severely than the ESPs when pumping a
two-phase mixture. The present study tested a 12 stage commercial helico-axial gas handler, referred as HGH. The
gas handler manufacturer, model, geometry and reference single-phase curves cannot be published due to a
confidentiality agreement. The two phase tests were carried out in a test bench at Labpetro β Cepetro β Unicamp using
water and air as working fluids. It was tested the effect of the rotation, mixture flow rate, gas volumetric fraction and
intake pressure on the developed pressure and torque. It is presented a dimensionless analysis for both the single and
two-phase pumping. The HGH developed pressure for the single-phase tests accomplish the affinity laws, similar to the
conventional ESP. The HGH pumped two-phase mixtures without surging for intake gas volumetric fractions as high
as 50%, however with a severe reduction in the developed pressure, efficiency, and operational range. Despite the
performance degradation, the HGH was able to tolerate gas fractions above the ESP. It is also shown how the mixture
flow rates and the developed pressures at the surging points are affected by the rotation, the intake pressure and the
intake gas volumetric fraction.
Keywords: helico-axial gas handler, two-phase pumping, bench test, petroleum industry, surging
1. INTRODUCTION
The main objective of the present study is to evaluate a 12-stage commercial helico-axial gas handler operating
with water and air in a horizontal test bench. The helico-axial gas handler, henceforth referred as HGH, is a rotary
machine used in the petroleum industry which tolerates a higher gas volumetric fraction than an ESP β electrical
submersible pump.
Centrifugal pumps are dynamic devices which increase the specific mechanical energy of a fluid. Due to well
diameter restrictions, the centrifugal pumps in the petroleum industry are multistage devices referred as ESP β electrical
submersible pumps. Each stage consists of an impeller and a diffuser.
The impeller (or rotor) has moving parts which increase the kinetic energy of the fluid. The diffuser (or stator)
partially converts the kinetic energy into pressure and drives the fluid to the inlet of the next ESP stage. The ESP is
originally designed to pump low viscosity liquids.
The ESP manufacturer usually provides the curves of the head (or the developed pressure), efficiency and brake
horse power (also known as mechanical power) per stage as a function of the liquid volumetric flow rate at a nominal
rotation. The liquid flow rate ranges from the open flow (no developed pressure) to the shut in (no flow rate) condition.
The head decreases with the liquid flow rate and the efficiency curve presents a maximum known as BEP β Best
Efficiency Point. These tests usually employ water as working fluid and accomplish the API β American Petroleum
Institute β recommended practices. They are corrected for a different rotation and liquid specific mass by applying
affinity or similarity laws, based on dimensional analysis. The affinity laws are valid only for single-phase low viscosity
liquids, such as water. For high viscosity fluids, including heavy oil, additional correction factors are necessary (e.g
Hydraulic Institute charts).
1.1 ESP Two-Phase Performance
The ESP can be installed either in the bottom hole of a production well or on the sea floor (e.g. skids). If the
pressure is below the bubble point a secondary gaseous phase is released.
The gas volumetric fraction ππ in a cross sectional area, such as the pump intake or outlet, is defined as the ratio
between the in situ gas ππ and the mixture ππππ₯ volumetric flow rates and given by Equation 1
ππ = ππ
ππππ₯
( 1 )
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The definition of ππ is based on the in situ volumetric flow rates through a cross area. It differs from the definition
of the gas hold up πΌπ, which is the ratio between the in situ volumes occupied by the gas π±π and the mixture π±πππ₯ in a
control volume, expressed by the following equation.
πΌπ = π±π
π±πππ₯
( 2 )
The ESP performance tends to degrade due to the gas phase. For low gas volumetric fractions ππ and high liquid
flow rates ππΏ the flow pattern in the ESP impeller is in dispersed bubbles (bubbly flow). The centrifugal force drives
the liquid towards the impeller periphery and reduces the gas phase velocity, causing a phase slippage. The gas tends to
lag the liquid. For higher gas volumetric fractions the phases separate in the impeller channels and the gas accumulates
in the impeller eye region. The accumulated gas reduces the effective flow area and changes the flow pattern to a
stratified or churn-like flow, deteriorating the pressure gain.
Empirical correlations based on the average performance of multi-stage pumps operating with two-phase mixtures
are specific for the geometry (pump model, diameter, and number of stages), rotation π, fluid properties (composition,
pressure and temperature), flow rate of each phase (or equivalently the mixture flow rate ππππ₯ and the gas volumetric
fraction ππ) , and flow pattern parameters at the pump intake (e.g. stochastic distribution of the bubble diameter ππ΅).
1.2 Surging, Gas Blocking and Gas Locking
Besides requiring a larger number of tests and more complex models to predict the ESP performance, the secondary
gas phase may cause undesired phenomena such as surging, gas blocking and gas locking.
In the performance test the ESP intake pressure πππ and the intake gas volumetric fraction ππ,ππ are kept constant,
while the liquid flow rate is reduced. The surging condition corresponds to the maximum developed pressure βπ, given
by Eq. ( 3 ):
(π βπ
πππππ₯,ππ)
πππ=ππ‘ππππ=ππ‘π
ππ’πππππ
= 0 ( 3 )
The surging phenomenon is related to system instabilities when the pump operates in a region where the
performance curve has a positive βπ(π) derivative. There are fluctuations in the pressures, flow rates, torque and motor
current.
The gas blocking is associated with severe performance degradation for low liquid flow rates due to the gas
accumulation along the impellers. The gas lock occurs when a stationary gas pocket inside the pump prevents the liquid
from flowing. The above definitions might change slightly depending on the author considered.
1.3 Gas Separator
Special devices known as gas separators are used in the petroleum industry in ESP equipped wells or subsea
boosting systems producing oil with free gas. The removed gas does not pass through the ESP and a secondary pipeline
is necessary. This option however may not be technically feasible or economically advantageous.
2. GAS HANDLER
The gas handler is an alternative to the gas separator. The gas handler is installed upstream the ESP with a common
shaft driven by the electric motor. Both the liquid and the free gas phases pass through the gas handler and then the
ESP. The main advantage of the gas handler compared to the gas separator is that it does not require an additional
pipeline to flow the separated gas.
The gas handler can perform different functions:
(i) A gas handler stage can be stable under intake conditions for which an ESP stage would be unstable (surging)
(ii) If both the gas handler and the ESP stages are stable, the gas handler can be more effective than the ESP in
terms of an objective function (developed pressure or efficiency).
(iii) The gas handler can also change the flow pattern parameters, fragmenting gas bubbles, in a process known as
gas mixing or homogenization. The gas handler can enhance the performance of the ESP and/or change the surging
point, enlarging the stable operational region. This phenomenon also occurs in a multistage ESP, since each stage
changes the flow pattern parameters delivered to the next one.
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Commercial gas handlers can have different physical principles and geometries. The gas handler performance
curves also tend to degrade for increasing gas volumetric fractions ππ, but less severely than for an ESP. On the other
hand, for single-phase or very low gas volumetric fraction ππ, the ESP can be more efficient than the gas handler.
2.1 AGH β Advanced Gas Handler
The Reda AGH β Advanced Gas Handler β has a slotted impeller and was studied by Romero (1999) e Monte
Verde (2011). None of the authors observed a significant improvement in the performance of an ESP installed
downstream the AGH.
Romero (1999) presented a map comparing the AGH and a conventional ESP (model GN4000) in terms of stability
(surging boundary) and developed head per stage. The author also developed a design procedure to select the best AGH
and ESP composition for a given intake condition. Monte Verde (2011) obtained the AGH performance curve and
visualized the two-phase flow using a high speed camera.
2.2 HGH β Helico-Axial Gas Handler
The HGH impeller has an internal conical hub connected to three helixes, increasing the kinetic energy of the fluid.
The diffuser partially converts the kinetic energy into pressure and drives the two-phase flow to the inlet of the next
HGH stage. There is no eye region, prone to gas accumulation, differing from a radial ESP. Figure 1 shows a
multiphase axial pump with an impeller similar to the HGH.
Figure 1. Semi-Axial Stage of a Multiphase Pump (Gulich, 2011)
The HGH geometry is not presented due to the confidentiality agreement. The HGH was not altered for flow
visualization in order to avoid changing the performance curves (clearances) and imposing operational constraints
(pressure and rotation).
3. SINGLE PHASE PUMPING THEORY
The mechanical power οΏ½οΏ½πππ (also known as BHP β brake horse power) and the single-phase hydraulic power οΏ½οΏ½βπ¦π
for a pump (ESP or HGH) are given by Eq. ( 4 ) and Eq. ( 5 ):
οΏ½οΏ½πππ = π ππ βπππ‘
( 4 )
οΏ½οΏ½βπ¦π = ππΏ Ξπ ( 5 )
where ππΏ is the liquid flow rate, Ξπ is the developed pressure, π is the rotation, and ππ βπππ‘ is the shaft torque.
The single-phase efficiency π is defined as the ratio between the hydraulic and the mechanical power, given by:
π =οΏ½οΏ½βπ¦π
οΏ½οΏ½πππ
( 6 )
3.1 Single-Phase Dimensionless Numbers
The Buckingham Pi theorem was used to determine the primitive dimensionless numbers governing the problem.
The independent variables were the fluid specific mass π, the rotation π, and the rotor diameter π·π . The dependent
variables were the liquid flow rate ππΏ , the developed pressure Ξπ, the mechanical power οΏ½οΏ½πππ , the viscosity π, the
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geometrical parameters πΏπ of the pump, and the superficial roughness π. Table 1shows the dimensionless numbers
obtained:
Table 1- Dimensionless Numbers for Single Phase Pumping
Specific Capacity ππΏ
β = ππΏ
π π·π3
( 7 )
Specific Developed Pressure Ξπβ =
Ξπ
π π2 π·π2
( 8 )
Specific Mechanical Power οΏ½οΏ½πππ
β =οΏ½οΏ½πππ
π π3 π·π5
( 9 )
Reynolds Number π π =
πππ·π2
π
( 10 )
Geometry Dimensionless Numbers πΏπ
β = πΏπ
π·π
( 11 )
Relative Roughness ν = π
π·π
( 12 )
The torque π and the mechanical power οΏ½οΏ½πππ are related to each other by the rotation π, which is an independent
variable of the dimensional analysis, resulting in the same dimensionless number.
During the tests the dimensionless geometry numbers πΏπβ were kept constant. The variation of the superficial
roughness π due to aging is assumed to be negligible. It is observed that for a single-phase low viscosity liquid the
Reynolds number π π does not play a relevant role. Therefore, for a given pump the specific head Ξπβ and the specific
brake horsepower οΏ½οΏ½πππβ can expressed as functions of only the specific capacity ππΏ
β.
The developed pressure Ξπ is directly proportional to the specific mass π. Defining a reference gravity acceleration
π, the single-phase developed head π» is defined by Eq. ( 13 ):
π» =Ξπ
π π
( 13 )
The single-phase efficiency π can be expressed in terms of the dimensionless numbers as:
π =ππΏ
β Ξπβ
οΏ½οΏ½πππβ
( 14 )
The primary dimensionless numbers specific capacity ππΏβ and specific developed pressure Ξπβ can be combined to
generate the specific speed πβ, a dimensionless number independent of the rotor diameter π·π and with a unitary
rotation π exponent, given by Eq. ( 15 ):
πβ =(ππΏ
β)12
(Ξπβ )34
=π ππΏ
12
(ππ»)34
( 15 )
The specific speed πβ is usually defined at the BEP β best efficiency point.
3.2 Single-Phase Normalization for a Low Viscosity Incompressible Fluid
For low viscosity liquids it is also possible to express the flow rate and the developed pressure in terms of
normalized variables. The normalized liquid flow rate ππΏπ is defined by Eq. ( 16 ) as the ratio between the liquid flow
rate ππΏ and the maximum flow rate ππ πππππβπβππ πππππβππππ€
at the same rotation π:
ππΏπ = ππΏ
ππ πππππβπβππ πππππβππππ€
( 16 )
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If the liquid specific mass π is constant, the normalized pressure Ξππ is defined by Eq. ( 17 ) as the ratio between
the developed pressure Ξπ and the shut-in pressure Ξππ πππππβπβππ ππ βπ’π‘βππ at the same rotation π.
Ξππ = Ξπ
Ξππ πππππβπβππ ππ βπ’π‘βππ for π = ππ‘π ( 17 )
If there is a change in the liquid specific mass π, it is more convenient to define a normalized head Hπ according to
Eq. ( 18 ):
Hπ = H
Hπ πππππβπβππ ππ βπ’π‘βππ
( 18 )
4. TWO-PHASE PUMPING THEORY
The mass and the volumetric flow rates of the mixture are given by the sum of the phase flow rates according to
Eq. ( 18 ) and Eq. ( 19 ):
ππππ₯ = ππΏ + ππ
( 19 )
οΏ½οΏ½πππ₯ = οΏ½οΏ½πΏ + οΏ½οΏ½π ( 20 )
The gas mass fraction ππ is defined as the ratio between the gas and the mixture mass flow rates, given by ( 21 ):
ππ = οΏ½οΏ½π
οΏ½οΏ½πππ₯
( 21 )
The massic οΏ½οΏ½ and the volumetric π flow rates of each phase are related to the specific mass π by:
οΏ½οΏ½π = ππππ
( 22 )
οΏ½οΏ½πΏ = ππΏππΏ ( 23 )
The liquid specific mass ππΏ is assumed to be constant (incompressible fluid, no thermal dilatation), whilst the gas
specific mass ππ is given by Eq. ( 24 ):
ππ =πππ£π ππππ
βπ’ π ππππ
( 24 )
where: ππ is the gas specific mass, πππ£π is the average molecular weight of the gas, βπ’ is the gas universal
constant, π is the gas compressibility factor, ππππ is the absolute pressure, and ππππ is the absolute temperature.
For the gas flow rate ππ, the mixture flow rates ππππ₯, and the gas volumetric fraction ππ it is necessary to specify
the thermodynamic condition considered (pressure π and temperature π). The average thermodynamic conditions
between the intake and the outlet are defined by Eq. ( 25 ) and Eq. ( 26 ):
πππ£π =πππ + πππ’π‘
2
( 25 )
πππ£π =πππ + πππ’π‘
2
( 26 )
where the subscripts have the following meanings: ππ for intke, ππ’π‘ for outlet, and ππ£π for the average
thermodynamic condition.
4.1 Two-Phase Isothermal Compression
The definition of two-phase isothermal head is based on Gulich (2011), although there is a difference in the
notation. It is assumed that there is no mass transfer between the phases, that the liquid and the gas are in thermal
equilibrium, and that the temperature variation caused by the compression is negligible for ππ < 80%. The
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thermodynamic process is approximated by an isothermal compression at the average temperature πππ£π between the
intake πππ and the outlet πππ’π‘ .
The power delivered to a mixture οΏ½οΏ½πππ₯ is assumed to be equal to the sum of the power delivered to the liquid and
to the gas phases according to Eq. ( 27 ):
οΏ½οΏ½πππ₯ = οΏ½οΏ½πΏ + οΏ½οΏ½π ( 27 )
As the head π» represents the increment of the fluid specific energy in terms of an equivalent elevation in a
reference gravitational field π, the power delivered to each phase is given by Eq. ( 28 ) and Eq. ( 29 ):
οΏ½οΏ½πΏ = οΏ½οΏ½πΏ π π»πΏ
( 28 )
οΏ½οΏ½π = οΏ½οΏ½π π π»π ( 29 )
In Eq. ( 28 ) and Eq. ( 29 ) the mass flow rates οΏ½οΏ½πΏ and οΏ½οΏ½π are constant. The equivalent head of each phase,
represented by π»πβππ π , is given by Eq. ( 30 ):
π»πβππ π =1
πβ«
πΏπ
ππβππ π
πππ’π‘
πππ
( 30 )
The symbol πΏπ indicates that the integral depends not only on the integration limits πππ and πππ’π‘ but also on the
thermodynamic process, since ππβππ π is a function of both the pressure π and the temperature π. Assuming that liquid
phase is incompressible (ππΏ = ππ‘π), the liquid head π»πΏ is given by Eq. ( 31 ):
π»πΏ = πππ’π‘ β πππ
π ππΏ
( 31 )
Assuming that the gas is ideal (π = 1), the gas phase isothermal head is given by:
π»π
π=πππ£π =
βπ’ πππ£ππππ
π ππ
ππ (πππ’π‘
πππ
ππππππ )
( 32 )
The two-phase isothermal head π»πππ₯
π=πππ£π is defined as:
π»πππ₯
π=πππ£π=
οΏ½οΏ½πππ₯
π=πππ£π
οΏ½οΏ½πππ₯ π=
οΏ½οΏ½πΏ π π»πΏ + οΏ½οΏ½π π π»π
π=πππ£π
οΏ½οΏ½πππ₯ π
( 33 )
Substituting Eq. ( 21 ) in Eq. ( 33 ) it is obtained Eq. ( 34 ):
π»πππ₯
π=πππ£π= (1 β ππ)π»πΏ + πππ»π
π=πππ£π ( 34 )
The two-phase isothermal efficiency π is defined by Eq. ( 35 ):
π =οΏ½οΏ½
πππ₯
π=πππ£π
οΏ½οΏ½πππ
( 35 )
4.2 Dimensionless Numbers for Two-Phase Pumping
The developed pressure Ξπ for a two-phase mixture is a function of the variables shown in Eq. ( 36 ) (Gamboa,
2008):
ΞππΊπππππ = π(ππΏ , ππ , ππΏ , ππ , π, π, π, ππΏ , ππ , π·π) ( 36 )
where π is the interfacial tension. The other parameters of Eq. ( 36 ) have already been defined. It is also possible to
include in the analysis the effect of the inclination π to the horizontal, the superficial roughness π and the geometrical
parameters πΏπ of the pump and the bench (e.g. nozzle diameters for gas injection, pipe diameter, etc), which might
IV Journeys in Multiphase Flows (JEM 2015)
affect the stochastic distribution of the flow pattern parameters. Besides the developed pressure Ξπ it might be of
interest the mechanical power Wπππ, also known as brake horse-power. Thus:
ΞP = π(ππΏ , ππ , ππΏ , ππ , π, π, π, ππΏ , ππ , π·π , π, π, πΏπ)
( 37 )
οΏ½οΏ½πππ = π(ππΏ , ππ , ππΏ , ππ , π, π, π, ππΏ , ππ , π·π , π, π, πΏπ) ( 38 )
In the present study the fluid properties and the gas flow rate are expressed at the intake conditions. A more
rigorous approach would considerer how the fluid properties change though the complete thermodynamic process
undergone by the mixture, requiring additional parameters (e.g. gas compressibility if non ideal, thermal dilatation
coefficient of the liquid, variation of the liquid viscosity with the temperature, etc.).
Adopting the liquid specific mass ππΏ , the rotation π, and the rotor diameter π·π as independent variables and
applying the Buckingham Pi theorem, the dimensionless numbers governing the problem are shown in Table 2:
Table 2 β Dimensionless Numbers for Two-Phase Pumping
Specific Developed Pressure Ξ 1,π = Ξπβ = Ξπ
π π2 π·π2 ( 39 )
Specific Mechanical Power Ξ 1,π = οΏ½οΏ½πππβ =
οΏ½οΏ½πππ
π π3 π·π5 ( 40 )
Gas to Liquid Specific Mass Ratio Ξ 2 =ππ
ππΏ
( 41 )
Reynolds Number for the Liquid Phase Ξ 3 =ππΏ
ππΏ π π·π2
=1
π ππΏ
( 42 )
Dimensionless Gas Viscosity Ξ 4 =ππ
ππΏ π π·π2
=ππ
ππΏ π ππΏ ( 43 )
Dimensionless Interfacial Tension Ξ 5 = πβ = π
π π2 π·π3 ( 44 )
Specific Gravitational Acceleration Ξ 6 = πβ = π
π2 π·π
( 45 )
Specific Liquid Capacity Ξ 7 = ππΏβ =
ππΏ
π π·π3 ( 46 )
Specific Gas Capacity Ξ 8 = ππβ =
ππ
π π·π3 ( 47 )
Inclination to Horizontal Ξ 9 = π ( 48 )
Specific Roughness Ξ 10 = ν = π
π·π
( 49 )
Dimensionless Geometric Parameters Ξ 11,π = πΏπβ =
πΏπ
π·π
( 50 )
The dimensionless numbers ππΏβ and ππ
β can be combined into the dimensionless numbers shown in Eq. ( 51 ) and
Eq. ( 52 ):
ππππ₯β = ππΏ
β + ππβ
( 51 )
ππ =ππ
β
ππππ₯β
( 52 )
where ππππ₯β is the specific mixture capacity and ππ is the gas volumetric fraction.
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4.3 Two-Phase Normalization
The two-phase normalized flow rates (liquid ππΏπ, gas πππ or mixture ππππ₯ π) and the normalized developed
pressure Ξππ are defined by Eq. ( 53 ) and Eq. ( 54 ):
ππ = π
ππ πππππβπβππ πππππβππππ€
( 53 )
Ξππ = Ξπ
Ξππ πππππβπβππ ππ βπ’π‘βππ
( 54 )
The gas volumetric fraction ππ is directly given by Eq.( 55 ) involving the normalized flow rates:
ππ = ππ π
ππππ₯ π
( 55 )
5. EXPERIMENTAL TESTS
The HGH water-air tests have been carried out in a horizontal bench at Unicamp β Cepetro β Labpetro. This bench
was used by Monte Verde (2011) to test the AGH.
5.1 Test Facilities
The HGH rotation π, constant for each curve, was set on the panel of a VSD β variable speed driver. The air was
supplied by the compression system of the laboratory. The water flows in a closed loop, being stored in a separation
tank. The water temperature was controlled by a chiller. The gas is injected into the liquid in a flange equipped with
four gas injectors placed upstream the HGH. The shaft passed through the injection flange.
5.2 Control Variables and Data Acquisition
The data acquisition software was implemented in Labiew (National Instruments). The opening ππ of the air valve
and the rotation ππ of the liquid booster were controlled via software. The pressure ππ upstream the gas valve was set
manually with two gas pressure regulators in tandem. The opening ππ of the valve installed downstream the HGH was
manually operated. The control variables are summarized in Table 3.
Table 3 β Control Variables
Variable Description Control
π HGH Rotation VSD Pannel
ππ Booster Booster-VSD via software
ππ Pressure upstream the gas valve Two manual regulators in Tandem
ππ Opening of the gas valve Via software
ππ Valve upstream the HGH Manual
The variables measured by the software are shown in Table 4:
Table 4 β Measured Variables
Variable Description Sensor
πππ Liquid temperature at the HGH inlet PT100
πππ’π‘ Mixture temperature at the HGH outlet PT100
πππ HGH Intake pressure Rosemount
πππ’π‘ HGH Outlet pressure Rosemount
ππ Pressure upstream the gas valve Rosenount
οΏ½οΏ½πΏ Liquid mass flow rate Coriolis
οΏ½οΏ½π Gas mass flow rate Coriolis
πππππ π’πππ Measured Torque Torquemeter
IV Journeys in Multiphase Flows (JEM 2015)
When the system reached a steady state condition (stable operation) or oscillation pattern (unstable operation)
satisfying the test nominal conditions (tolerance about 1%) the variables were sampled during 30 seconds at a sample
rate equal to 4 kHz. The arithmetic mean values and standard deviations of each variable were saved in a text file
(*.lvm extension).
5.3 Residual Torque
The residual torque corresponds to the measured torque when no pump is being driven by the motor. It is assumed
that when the motor is driving the HGH the corrected shaft torque is given by the difference between the measured
torque and the residual torque at the same rotation, as expressed by Eq. ( 56 ):
ππ βπππ‘_πππππππ‘ππ = πππππ π’πππ β ππππ πππ’ππ ( 56 )
where: πππππ π’πππ is the measured torque, ππππ πππ’ππ is the residual torque (no mechanical load), and ππ βπππ‘_πππππππ‘ππ
is the corrected shaft torque
The residual torque is associated with the bench bearings between the electrical motor and the HGH. This torque is
a function of the HGH rotation π, the axial load πΉππ₯πππ , and the temperature πππ’π of the lubrication fluid. The effect of
the axial load is neglected. It is assumed that the temperature of the lubrication fluid πππ’π depends basically upon the
rotation. The HGH corrected shaft torque ππ βπππ‘_πππππππ‘ππ is used to calculate the average torque per stage ππ π‘π
according to Eq. ( 57 ):
ππ π‘π = ππ βπππ‘_πππππππ‘ππ
ππ π‘π
( 57 )
where: ππ π‘π is the average torque per stage and ππ π‘π is the number of stages.
5.4 Single-Phase Tests
For the single-phase tests there is no gas injection (ππ = 0; ππ = 0) and the intake pressure πππ does not have
to be controlled, providing the bench operational constraints are respected. The liquid flow rate ππΏ ranged from slightly
above the open-flow (Ξπ = 0) to the shut-in (ππΏ = 0) condition.
5.5 Two-Phase Test Procedure
The performance tests consist in decreasing the liquid flow rate ππΏ for a constant rotation π, intake pressure πππ
and either gas volumetric flow rate ππ,ππ or the gas volumetric fraction ππ,ππ at the HGH intake.
For each curve the inlet mixture flow rate ππππ₯,ππ started slightly above the open-flow (no developed pressure) and
was reduced until an unstable condition was reached. The inlet mixture flow rate ππππ₯,ππ was reduced by closing the
manual valve ππ downstream the HGH. Then the rotation ππ of the VSD liquid booster, the gas valve opening ππ
and/or the regulated gas pressure ππ were adjusted.
6. EXPERIMENTAL RESULTS
The following sections show the experimental results.
6.1 Residual Torque Test
The figure below shows the residual torque obtained for different rotations in both directions and a parabolic
polynomial fitting calculated by the Solver (Excel).
CΓ©sar Longhi Experimental Study of a Multistage Helico-Axial Gas Handler operating with Water and Air
10
Figure 2 β Residual torque
6.2 Single-Phase Tests
The single-phase tests using water as working fluid were performed at π = 2100, 2600, 3000, and 3600 rpm. The
manufacturer reference curves are not presented due to the confidentiality agreement.
Figure 3 β Developed pressure and measured torque for single-phase tests at 2100, 2600, 3000, and 3600 rpm
The following figures show the single-phase HGH performance per stage after correcting the measured torque:
Figure 4 β Average developed pressure and corrected average torque per stage for single-phase tests
y = 9.81409E-08x2 - 1.22493E-05x + 7.12870E-01RΒ² = 9.61430E-01
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 500 1000 1500 2000 2500 3000 3500 4000
Re
sid
ual
To
rqu
e [
N.m
]
Rotation [ RPM ]
Residual Torque Test
HGH Direction
Oposite Direction
-400
-200
0
200
400
600
800
1000
1200
1400
0 100 200 300 400 500 600 700 800
ΞP
[ k
Pa
] -
Pre
ssu
re In
cre
me
nt
QL [mΒ³/day] - Liquid Flowrate
HGH Single Phase
Ο=3600 rpm
Ο=3000 rpm
Ο=2600 rpm
Ο=2100 rpm
0
5
10
15
20
25
0 100 200 300 400 500 600 700 800
Ο_m
eas
ure
d [
N.m
] -
Me
asu
red
To
rqu
e
QL [mΒ³/day] - Liquid Flowrate
HGH Single Phase
Ο=3600 rpm
Ο=3000 rpm
Ο=2600 rpm
Ο=2100 rpm
-40
-20
0
20
40
60
80
100
120
0 100 200 300 400 500 600 700 800
ΞP
[ k
Pa/
stag
e ]
-A
vera
ge P
ress
ure
Incr
em
en
t p
er
Stag
e
QL [mΒ³/day] - Liquid Flowrate
HGH Single Phase
Ο=3600 rpm
Ο=3000 rpm
Ο=2600 rpm
Ο=2100 rpm
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0 100 200 300 400 500 600 700 800
Ο_st
g [N
.m]
-A
vega
re T
orq
ue
pe
r St
age
QL [mΒ³/day] - Liquid Flowrate
HGH Single Phase
Ο=3600 rpm
Ο=3000 rpm
Ο=2600 rpm
Ο=2100 rpm
IV Journeys in Multiphase Flows (JEM 2015)
Figure 5 β Average mechanical power per stage and efficiency for single-phase tests
The following figures show the single-phase HGH test results in terms of the dimensionless numbers ππΏβ, βπβ ,
οΏ½οΏ½πππβ , πβ , and the efficiency π:
Figure 6 β Dimensionless Numbers for the single-phase tests: (a) specific head per stage; (b) specific brake horse-
power; (c) efficiency as a function of the specific capacity; (d) efficiency as a function of the specific speed.
As there was a good agreement in the βπβ(ππΏβ) plots for the different rotations π, the effect of the Reynolds
number π π seems to be negligible. The differences in the specific brake horsepower οΏ½οΏ½πππβ and efficiency π might have
been caused by the torque inaccuracy.
The following figures show the single-phase test results expressed in terms of normalized flow rate ππΏ π,
normalized pressure βππ and efficiency π:
0
100
200
300
400
500
600
700
0 100 200 300 400 500 600 700 800
αΊ_m
ec_
stg
[ W
att/
stg
] -
Ave
rage
BH
P M
ech
anic
al
Po
we
r p
er
HG
H-S
tage
QL [mΒ³/day] - Liquid Flowrate
HGH Single Phase
Ο=3600 rpm
Ο=3000 rpm
Ο=2600 rpm
Ο=2100 rpm
0%
10%
20%
30%
40%
50%
60%
0 100 200 300 400 500 600 700 800
Ξ· [
% ]
-Ef
fici
en
cy
QL [mΒ³/day] - Liquid Flowrate
HGH Single Phase
Ο=3600 rpm
Ο=3000 rpm
Ο=2600 rpm
Ο=2100 rpm
0.0E+00
2.0E-02
4.0E-02
6.0E-02
8.0E-02
1.0E-01
1.2E-01
0.0E+00 5.0E-03 1.0E-02 1.5E-02 2.0E-02 2.5E-02 3.0E-02 3.5E-02 4.0E-02 4.5E-02
ΞP
* -
Spe
cifi
c H
ead
pe
r St
age
QL* - Specific Liquid Capacity
HGH Single Phase
Ο=3600 rpm
Ο=3000 rpm
Ο=2600 rpm
Ο=2100 rpm
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
2.5E-03
3.0E-03
3.5E-03
0.0E+00 5.0E-03 1.0E-02 1.5E-02 2.0E-02 2.5E-02 3.0E-02 3.5E-02 4.0E-02 4.5E-02
αΊ_m
ec*
-Sp
eci
fic
Bre
ak H
ors
ep
ow
er
pe
r St
age
QL* - Specific Liquid Capacity
HGH Single Phase
Ο=3600 rpm
Ο=3000 rpm
Ο=2600 rpm
Ο=2100 rpm
0%
10%
20%
30%
40%
50%
60%
0.0E+00 5.0E-03 1.0E-02 1.5E-02 2.0E-02 2.5E-02 3.0E-02 3.5E-02 4.0E-02 4.5E-02
Ξ· [
% ]
-Ef
fici
en
cy
QL* - Specific Liquid Capacity
HGH Single Phase
Ο=3600 rpm
Ο=3000 rpm
Ο=2600 rpm
Ο=2100 rpm
0%
10%
20%
30%
40%
50%
60%
1.0E-01 1.0E+00 1.0E+01 1.0E+02
Ξ· [
% ]
-Ef
fici
en
cy
N* - Specific Speed
HGH Single Phase
Ο=3600 rpm
Ο=3000 rpm
Ο=2600 rpm
Ο=2100 rpm
CΓ©sar Longhi Experimental Study of a Multistage Helico-Axial Gas Handler operating with Water and Air
12
Figure 7 β Normalized Pressure and efficiency as a function of the normalized flow rate for the single-phase tests
6.3 Two-Phase Tests with Constant Gas Volumetric Flow rate at the Intake
The following figures show the performance curves with ππ,ππ = ππ‘π obtained at three different rotations (π =
2600 rpm, 3000 rpm, and 3600 rpm) for the same intake pressure πππ = 300 πππ.
Figure 8 β Effect of the gas flow rate and rotation on the average developed pressure per stage for a constant gas
intake pressure
The developed pressure degraded mildly for low gas ππ and high liquid ππΏ flow rates, normally corresponding to a
homogeneous two-phase mixture (no visualization to confirm). The developed pressure degraded more severely for
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
(ΞP/
ΞP
_sp
_max
) -
No
rmal
ize
d P
ress
ure
(QL/Qmax) - Normalized Liquid Flowrate
HGH Single Phase
Ο=3600 rpm
Ο=3000 rpm
Ο=2600 rpm
Ο=2100 rpm
BEP @ Ο = 3600 rpm
0%
10%
20%
30%
40%
50%
60%
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ξ· [
% ]
-Ef
fici
en
cy
(QL/Qmax) - Normalized Liquid Flowrate
HGH Single Phase
Ο=3600 rpm Ο=3000 rpm Ο=2600 rpm Ο=2100 rpm BEP @ Ο = 3600 rpm
0
10
20
30
40
50
60
0 50 100 150 200 250 300 350 400 450 500
ΞP
[ k
Pa/
stag
e ]
-A
vera
ge P
ress
ure
Incr
em
en
t p
er
Stag
e
Qmix_in [mΒ³/day] - Intake Volumetric Mixture Flowrate
HGH Performance Test - Ο = 2600 rpm - P_in=300 kPa - Qg_in=cte
Single Phase
Qg_in=24.6 mΒ³/day
Qg_in=49.54 mΒ³/day
Qg_in=74.39 mΒ³/day
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600
ΞP
[ k
Pa/
stag
e ]
-A
vera
ge P
ress
ure
Incr
em
en
t p
er
Stag
e
Qmix_in [mΒ³/day] - Intake Volumetric Mixture Flowrate
HGH Performance Test - Ο = 3000 rpm - P_in=300 kPa - Qg_in=cte
Single Phase
Qg_in=28.3 mΒ³/day
Qg_in=57.2 mΒ³/day
Qg_in=85.8 mΒ³/day
0
20
40
60
80
100
120
0 100 200 300 400 500 600 700
ΞP
[ k
Pa/
stag
e ]
-A
vera
ge P
ress
ure
Incr
em
en
t p
er
Stag
e
Qmix_in [mΒ³/day] - Intake Volumetric Mixture Flowrate
HGH Performance Test - Ο = 3600 rpm - P_in=300 kPa - Qg_in=cte
Single Phase
Qg_in=17 mΒ³/day
Qg_in=34 mΒ³/day
Qg_in=51.5 mΒ³/day
Qg_in=68.6 mΒ³/day
Qg_in=90 mΒ³/day
Qg_in=103 mΒ³/day
Qg_in=128.6 mΒ³/day
IV Journeys in Multiphase Flows (JEM 2015)
higher gas flow rates ππ. For low liquid flow rates ππΏ the system became unstable even for moderate gas flow rates ππ.
No gas lock was observed.
Effect of the Rotation π for πΈπ,ππ = πππ
The three curves in the following figure have the same normalized gas volumetric flow rate ππ ππ,π = 0.1568 at the
HGH intake:
Figure 9 β Effect of the rotation on the average developed pressure for a constant intake pressure 300 kPa and
normalized gas flow rate πππ,ππ = 0.1568
The effect of the rotation π is evaluated by expressing the data in terms of the normalized mixture flow rate ππππ₯ π
and the normalized developed pressure Ξππ:
Figure 10 Effect of the rotation on the normalized average developed pressure and on the outlet gas volume fraction
for a constant intake pressure 300 kPa and normalized gas flow rate πππ,ππ = 0.1568
If the mixture flow rate is below the open-flow (positive pressure gain condition), a higher rotation π is associated
with a lower gas volumetric fraction ππ,ππ’π‘ at the outlet and with a higher normalized pressure Ξππ. As the normalized
gas volumetric flow rate ππ ππ,π at the inlet is constant for each curve, the inlet gas volumetric fraction ππ,ππ decreases
monotonically with the normalized mixture flow rate ππππ₯ ππ,π. The outlet ππ,ππ’π‘ and the intake ππ,ππ gas volumetric
fractions are equal for the open-flow condition. No effect of the rotation π on the open-flow condition was observed.
6.4 Two-Phase Tests with Constant Gas Volumetric Fraction at the Intake
The following figures show the test results for a constant intake pressure (πππ = 300 πππ) varying the intake gas
volumetric fraction ππ ππ for three different rotations (π = 2600, 3000, and 3600 rpm):
0
5
10
15
20
25
30
35
40
45
50
250.0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 650.0 700.0 750.0
ΞP
[ k
Pa/
stag
e ]
-A
vera
ge P
ress
ure
Incr
em
en
t p
er
Stag
e
Qmix_in [mΒ³/day] - Intake Volumetric Mixture Flowrate
HGH Performance Test - P_in=300 kPa - Qg_in_d=0.1568
Ο=2600 rpm - Qg_in=74.39 mΒ³/day
Ο=3000 rpm - Qg_in=85.8 mΒ³/day
Ο=3600 rpm - Qg_in=103 mΒ³/day
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
(ΞP/
ΞP
_sp
_max
) -
No
rmal
ize
d P
ress
ure
(Qmix_in/Q_sp_max) - Normalized Inlet Mixture Flowrate
HGH Performance Test - P_in=300 kPa - Qg_in_d=0.1568
Single Phase
Ο=2600 rpm - Qg_in=74.39 mΒ³/day
Ο=3000 rpm - Qg_in=85.8 mΒ³/day
Ο=3600 rpm - Qg_in=103 mΒ³/day
0%
5%
10%
15%
20%
25%
30%
0%
5%
10%
15%
20%
25%
30%
0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Ξ»_o
ut
[ %
] -
Ou
tlet
GV
F
Ξ»_in
[ %
] -
Inle
t G
VF
(Qmix_in/Q_sp_max) - Normalized Inlet Mixture Flowrate
HGH Performance Test - P_in=300 kPa - Qg_in_d=0.1568
Ξ»_in [ % ] - Ο=2600 rpm - Qg_in=74.39 mΒ³/day Ξ»_in [ % ] - Ο=3000 rpm - Qg_in=85.8 mΒ³/day
Ξ»_in [ % ] - Ο=3600 rpm - Qg_in=103 mΒ³/day Ξ»_out [ % ] - Ο=2600 rpm - Qg_in=74.39 mΒ³/day
Ξ»_out [ % ] - Ο=3000 rpm - Qg_in=85.8 mΒ³/day Ξ»_out [ % ] - Ο=3600 rpm - Qg_in=103 mΒ³/day
CΓ©sar Longhi Experimental Study of a Multistage Helico-Axial Gas Handler operating with Water and Air
14
Figure 11 β Effect of the rotation and intake gas volumetric fraction on the average developed pressure
In the three previous figures, as the intake gas volumetric fraction ππ ππ increases, the surging point occurs at a
higher inlet mixture flow rate ππππ₯ πππ π’πππππ
and corresponds to a lower developed pressure Ξππ π’πππππ. For a higher gas
volumetric fraction ππ,ππ at the intake there was also a reduction in the inlet mixture flow rate in the open-flow
condition, represented by ππππ₯ ππππππβππππ€
.
Effect of the Intake Pressure π·ππ for π = ππππ πππ and ππ,ππ = ππ%
The following figure shows the effect of the intake pressure πππ for π = 3600 πππ and πππ = 30%:
Figure 12 β Effect of the intake pressure (100, 200, 300, and 400 kPa) on the gas-to-liquid specific mass ratio and
on the outlet gas volumetric fraction for a constant rotation (3600 rpm) and intake gas volumetric fraction (30%)
0
10
20
30
40
50
60
0 50 100 150 200 250 300 350 400 450 500
ΞP
[ k
Pa/
stag
e ]
-A
vera
ge P
ress
ure
Incr
em
en
t p
er
Stag
e
Qmix_in [mΒ³/day] - Intake Volumetric Mixture Flowrate
HGH Performance Test - Ο = 2600 rpm - P_in=300 kPa - Ξ»_in=cte
Single Phase
Ξ»_in=10 %
Ξ»_in=20 %
Ξ»_in=30 %
Ξ»_in=40 %
Ξ»_in=50 %
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600
ΞP
[ k
Pa/
stag
e ]
-A
vera
ge P
ress
ure
Incr
em
en
t p
er
Stag
e
Qmix_in [mΒ³/day] - Intake Volumetric Mixture Flowrate
HGH Performance Test - Ο = 3000 rpm - P_in=300 kPa - Ξ»_in=cte
Single Phase
Ξ»_in=10 %
Ξ»_in=20 %
Ξ»_in=30 %
Ξ»_in=40 %
Ξ»_in=50 %
0
20
40
60
80
100
120
0 100 200 300 400 500 600 700
ΞP
[ k
Pa/
stag
e ]
-A
vera
ge P
ress
ure
Incr
em
en
t p
er
Stag
e
Qmix_in [mΒ³/day] - Intake Volumetric Mixture Flowrate
HGH Performance Test - Ο = 3600 rpm - P_in=300 kPa - Ξ»_in=cte
Single Phase
Ξ»_in=5 %
Ξ»_in=10 %
Ξ»_in=20 %
Ξ»_in=30 %
Ξ»_in=40 %
Ξ»_in=45 %
0.0E+00
2.0E-03
4.0E-03
6.0E-03
8.0E-03
1.0E-02
300 400 500 600 700 800
(Οg_
avg
/ΟL)
-G
as-L
iqu
id Ο
Rat
io a
t A
vera
ge
The
rmo
dyn
amic
Co
nd
itio
ns
Qmix_in [mΒ³/day] - Intake Volumetric Mixture Flowrate
HGH Performance Test - Ο = 3600 rpm - Ξ»_in=30 %
P_in=100 kPa
P_in=200 kPa
P_in=300 kPa
P_in=400 kPa -Partial
0%
5%
10%
15%
20%
25%
30%
35%
300 350 400 450 500 550 600 650 700
Ξ»_o
ut
[ %
] -
Ou
tlet
GV
F
Qmix_in [mΒ³/day] - Intake Volumetric Mixture Flowrate
HGH Performance Test - Ο = 3600 rpm - Ξ»_in=30 %
P_in=100 kPa
P_in=200 kPa
P_in=300 kPa
P_in=400 kPa -Partial
IV Journeys in Multiphase Flows (JEM 2015)
Figure 13 - Effect of the intake pressure on the average developed pressure
The curve with πππ = 400 πππ could not reach higher flow rates due to limitations in the gas injection. The
developed pressure Ξπ curves are similar, although the surging point occurred at lower mixture flow rates ππππ₯ πππ π’ππππ
for
higher intake pressures πππ . If the mixture flow rate is below the open-flow (positive pressure gain condition), a higher
intake pressure πππ corresponds to a lower gas volumetric fraction πππ’π‘ at the outlet. It also corresponds to a higher
average gas to liquid specific mass ratio, represented by (ππ,ππ£π
ππΏβ ).
Effect of the Rotation π for π·ππ = πππ ππ·π and ππ,ππ = ππ%
Figure 14 shows that for high mixture flow rates and low intake gas volumetric fractions (ππ,ππ = 10%) there was
only a mild degradation in the two-phase developed pressure compared to the single-phase reference. The gas phase
also causes a reduction in the two phase isothermal efficiency, as shown in the following figure:
Figure 14 β Effect of the rotation (2600, 3000, and 3600 rpm) on the average developed pressure for a constant
intake pressure (300 kPa) and gas volumetric fraction (10%)
0
5
10
15
20
25
30
35
300 350 400 450 500 550 600 650 700
ΞP
[ k
Pa/
stag
e ]
-A
vera
ge P
ress
ure
Incr
em
en
t p
er
Stag
e
Qmix_in [mΒ³/day] - Intake Volumetric Mixture Flowrate
HGH Performance Test - Ο = 3600 rpm - Ξ»_in=30 %
Single Phase
P_in=100 kPa
P_in=200 kPa
P_in=300 kPa
P_in=400 kPa -Partial
-40
-20
0
20
40
60
80
100
120
0 100 200 300 400 500 600 700 800
ΞP
[ k
Pa/
stag
e ]
-A
vera
ge P
ress
ure
Incr
em
en
t p
er
Stag
e
Qmix [mΒ³/day] - Inlet Volumetric Flowrate
HGH Performance Test - P1=300 kPa - Ξ»_inlet=10 %
Single Phase Ο=3600 rpm
Single Phase Ο=3000 rpm
Single Phase Ο=2600 rpm
Ο=3600 rpm - Ξ»_inlet=10 %
Ο=3000 rpm - Ξ»_inlet=10 %
Ο=2600 rpm - Ξ»_inlet=10 %
Surging [Max ΞP for Ξ»_in=cte; P_in=cte]
CΓ©sar Longhi Experimental Study of a Multistage Helico-Axial Gas Handler operating with Water and Air
16
Figure 15 β Effect of the rotation (2600, 3000, and 3600 rpm) on the efficiency for a constant intake pressure
(300 kPa) and gas volumetric fraction (10%)
Effect of the Rotation π for π·ππ = πππ ππ·π and ππ,ππ = ππ%
The following figures show the normalized developed pressure Ξππ and the outlet gas volumetric fraction ππ,ππ’π‘ as
a function of the normalized mixture intake flow rate ππππ₯ ππ,π for πππ = 300 πππ and ππ,ππ = 30% at three different
rotations (π = 2600, 3000, and 3600 rpm).
Figure 16 β Effect of the rotation (2600, 3000, and 3600 rpm) on the normalized pressure and outlet gas volumetric
fraction for a constant intake pressure (300 kPa) and gas volumetric fraction (10%)
The outlet gas volumetric fraction ππ,ππ’π‘ decreases and the normalized pressure Ξππ increases for a higher rotation
π. The surging point at a higher rotation occurs at a lower inlet normalized mixture folwrate ππππ₯ ππ,ππ π’πππππ
and corresponds
to a higher normalized developed pressure Ξπππ π’πππππ
. This was also observed for different gas intake volumetric
fractions ππ,ππ.
6.5 Surging Points
The surging points shown in Table 5 correspond to the maximum developed pressure samples βπ obtained for each
performance test with constant ππ,ππ gas volumetric fraction at the intake.
0%
10%
20%
30%
40%
50%
60%
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ξ· [
% ]
-Tw
o-P
has
e E
ffic
ien
cy
(Qmix_avg/Qmax) - Normalized Mixture Flowrate at Average Thermodynamic Conditions
HGH Performance Test - P1=300 kPa - Ξ»_inlet=10 %
Single Phase Ο=3600 rpm Single Phase Ο=3000 rpm Single Phase Ο=2600 rpm
Ο=3600 rpm - Ξ»_inlet=10 % Ο=3000 rpm - Ξ»_inlet=10 % Ο=2600 rpm - Ξ»_inlet=10 %
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
(ΞP/
ΞP
_sp
_max
) -
No
rmal
ize
d P
ress
ure
(Qmix_in/Q_sp_max) - Normalized Inlet Mixture Flowrate
HGH Performance Test - P_in=300 kPa - Ξ»_in=30 %
Single Phase
Ο=3600 rpm
Ο=3000 rpm
Ο=2600 rpm
0%
5%
10%
15%
20%
25%
30%
35%
0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
Ξ»_o
ut
[ %
] -
Ou
tlet
GV
F
(Qmix_in/Q_sp_max) - Normalized Inlet Mixture Flowrate
HGH Performance Test - P_in=300 kPa - Ξ»_in=30 %
Ο=3600 rpm
Ο=3000 rpm
Ο=2600 rpm
IV Journeys in Multiphase Flows (JEM 2015)
Table 5 β Surging Points
Analyzing the data, none of the two-phase dimensionless numbers Ξ π was constant at the surging points. Figure 17
and Figure 18 show the normalized inlet mixture flow rate ππππ₯ ππ,ππ π’πππππ
and the normalized developed pressure Ξπππ π’πππππ
at the surging points represented as functions of the inlet gas volumetric fraction ππ,ππ:
Figure 17 β Normalized inlet mixture flow rate at the surging points as a function of the inlet gas volumetric
fraction
Ο [rpm] P_in [ kPa ] Ξ»_in [% ] P1 [kPa] QL [mΒ³/day] Qm_1 [mΒ³/day] Ξ»_1 [ % ] ΞP_12 [ kPa ] Qm1_d ΞP_12_d
2600 300 10% 299.51 111.58 123.29 9.5% 445.59 2.60E-01 0.7019
2600 300 20% 299.45 183.89 229.09 19.7% 235.47 4.83E-01 0.3709
2600 300 30% 299.88 202.87 290.67 30.2% 139.30 6.13E-01 0.2194
2600 300 40% 299.66 193.70 321.93 39.8% 92.50 6.79E-01 0.1457
2600 300 50% 300.10 175.31 352.83 50.3% 46.13 7.44E-01 0.0727
3000 300 10% 300.14 136.87 152.10 10.0% 620.89 2.78E-01 0.7347
3000 300 20% 301.07 221.13 275.82 19.8% 345.99 5.04E-01 0.4094
3000 300 30% 300.59 226.83 323.88 30.0% 204.82 5.92E-01 0.2424
3000 300 40% 299.14 216.09 361.09 40.2% 131.91 6.60E-01 0.1561
3000 300 50% 298.58 202.83 409.77 50.5% 68.55 7.49E-01 0.0811
3600 100 30% 100.64 271.92 387.48 29.8% 326.11 5.90E-01 0.2680
3600 200 30% 200.69 267.15 379.52 29.6% 337.90 5.78E-01 0.2777
3600 300 5% 298.54 120.21 126.56 5.0% 1058.98 1.93E-01 0.8702
3600 300 10% 299.21 155.89 173.00 9.9% 938.85 2.63E-01 0.7714
3600 300 15% 299.75 168.79 198.59 15.0% 802.22 3.02E-01 0.6592
3600 300 20% 300.07 181.17 226.29 19.9% 613.14 3.45E-01 0.5038
3600 300 25% 301.17 216.78 287.61 24.6% 461.53 4.38E-01 0.3792
3600 300 30% 300.17 252.60 359.80 29.8% 355.75 5.48E-01 0.2923
3600 300 40% 299.65 243.48 403.98 39.7% 226.73 6.15E-01 0.1863
3600 300 45% 299.79 241.74 439.88 45.0% 171.12 6.70E-01 0.1406
3600 400 30% 400.32 251.39 358.32 29.8% 369.94 5.46E-01 0.3040
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0% 10% 20% 30% 40% 50% 60%
(Qm
ix_i
n/Q
_sp
_max
) -
No
rmal
ize
d In
let
Mix
ture
Fl
ow
rate
at
Surg
ing
Ξ»_in [ % ] - Inlet GVF
HGH Performance Test - Surging Condition
(Ο = 2600 rpm; P_in = 300 kPa)
(Ο = 3000 rpm; P_in = 300 kPa)
(Ο = 3600 rpm; P_in = 300 kPa)
(Ο = 3600 rpm; Ξ»_in = 30%; P_in = 100, 200, 300, and 400 kPa)
CΓ©sar Longhi Experimental Study of a Multistage Helico-Axial Gas Handler operating with Water and Air
18
Figure 18 β Normalized developed pressure at the surging points as a function of the inlet gas volumetric fraction
The surging normalized mixture flow rate ππππ₯ ππ,ππ π’πππππ
decreases and that the normalized developed pressure
Ξπππ π’πππππ
increases as the rotation π increases. There was a higher dispersion for ππ ππ = 20% samples compared to
the other gas volumetric fractions of the test matrix.
Comparison between the Surging Points and the Single-Phase Curve
The following figure compares the surging points to the single-phase curve in terms of normalized flow rates and
developed pressure. The region of stable operation is on the right of the surging points.
Figure 19 β Comparison between the single-phase and the surging points normalized curves
Comparison between Surging Point and Tests with πΈπ,ππ = πππ for π = ππππ πππ and π·ππ = πππ ππ·π
The figure below shows that the points with maximum Ξπ in the curves with ππ,ππ = ππ‘π do not correspond to the
surging points obtained in the ππ ππ = ππ‘π tests for the same rotation (π = 3600 πππ) and intake pressure (πππ =
300 πππ):
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0% 10% 20% 30% 40% 50% 60%
(ΞP/
ΞP
_sp
_max
) -
No
rmal
ize
d P
ress
ure
at
Surg
ing
Ξ»_in [ % ] - Inlet GVF
HGH Performance Test - Surging Condition
(Ο = 2600 rpm; P_in = 300 kPa)
(Ο = 3000 rpm; P_in = 300 kPa)
(Ο = 3600 rpm; P_in = 300 kPa)
(Ο = 3600 rpm; Ξ»_in = 30%; P_in = 100, 200, 300, and 400 kPa)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.2 0.4 0.6 0.8 1.0 1.2
(ΞP/
ΞP
_sp
_max
) -
No
rmal
ize
d P
ress
ure
at
Surg
ing
(Qmix_in/Q_sp_max) - Normalized Inlet Mixture Flowrate
HGH Performance Test - Surging Condition
Single Phase
(Ο = 2600 rpm; P_in = 300 kPa)
(Ο = 3000 rpm; P_in = 300 kPa)
(Ο = 3600 rpm; P_in = 300 kPa)
(Ο = 3600 rpm; Ξ»_in = 30%; P_in = 100, 200, 300, and 400 kPa)
IV Journeys in Multiphase Flows (JEM 2015)
Figure 20 β Comparison between the surging points and the curves with constant intake gas volumetric flow rate at
rotation 3600 rpm and intake pressure 300 kPa
The points of maximum Ξπ are very close only for the ππ,ππ = 10% and ππ,ππ = 17 π3 πππ¦β tests. For higher gas
volumetric flow rates ππ,ππ = ππ‘π, the points of maximum Ξπ are in a region between the single-phase curve and an
interpolated curve passing through the surging points (ππ,ππ = ππ‘π), the region of stable operation.
Preliminary Surging Correlation
The first attempt to find a surging correlation for the 12-stage HGH assumed that the intake gas volumetric fraction
at the surging point, represented as ππ,πππ π’πππππ
, could be expressed as the product of independent functions of the
following arguments: the rotation π; the normalized intake mixture flow rate ππππ₯ ππ,π ; and the gas to liquid specific
mass ratio at the intake, represented as ππ ππ
ππΏβ . Therefore:
οΏ½οΏ½π,πππ π’πππππ
= π1(ππππ₯ ππ,π ) ππ1 (ππ ππ
ππΏ
)
π2
( 58 )
where:
π1(ππππ₯ ππ,π ) = β ππ
3
π=0
ππππ₯ ππ,π π
( 59 )
Assuming οΏ½οΏ½π,πππ π’πππππ
= 0 for ππππ₯ ππ,π π π’ππππ
= 0, the general solution is π0 = 0. The fitting coefficients ππ (for π = 1 to
3), π1 and π2 were calculated by the Solver (Excel) minimizing the accumulated quadratic error πΈ defined as:
πΈ = β(οΏ½οΏ½π,πππ π’πππππ
β ππ,πππ π’πππππ
)2
( 60 )
The following figure shows the original values ππ,πππ π’πππππ
(horizontal-axis) and the correlation prediction οΏ½οΏ½π,πππ π’πππππ
(vertical-axis).
0
20
40
60
80
100
120
0 100 200 300 400 500 600 700 800
ΞP
[ k
Pa/
stag
e ]
-A
vera
ge P
ress
ure
Incr
em
en
t p
er
Stag
e
Qmix_in [mΒ³/day] - Intake Volumetric Mixture Flowrate
HGH Performance Test - Ο = 3600 rpm - P_in = 300 kPa
Single Phase
Qg_in = 17 mΒ³/day - Qg_in_d=0.0259
Qg_in = 34 mΒ³/day - Qg_in_d=0.0518
Qg_in = 51.5 mΒ³/day - Qg_in_d=0.0784
Qg_in = 68.6 mΒ³/day - Qg_in_d=0.1045
Qg_in = 90 mΒ³/day - Qg_in_d=0.137
Qg_in = 103 mΒ³/day - Qg_in_d=0.1568
Qg_in = 128.6 mΒ³/day - Qg_in_d=0.1958
Surging (Ο = 3600 rpm; P_in = 300 kPa)
CΓ©sar Longhi Experimental Study of a Multistage Helico-Axial Gas Handler operating with Water and Air
20
Figure 21 β Errors of the preliminary correlation for the inlet gas volumetric fraction at the surging point
There was a very poor fitting around ππ ππ = 20%. It is therefore necessary to refine the test matrix around
ππ ππ = 20% and to adjust the coefficients of different base functions.
6.6 Two-Phase Efficiency
The figure below shows the HGH two-phase efficiency π as a function of the inlet mixture volumetric flow rate
ππππ₯,ππ for π = 3600 πππ and πππ = 300 πππ:
Figure 22 β Two-phase efficiency curves for rotation 3600 rpm, intake pressure 300 kPa, and inlet gas volumetric
fraction ranging from 0 to 45%
For a given intake mixture flow rate ππππ₯ ππ£π the two-phase efficiency π decreases as the inlet gas volumetric
fraction ππ ππ increases.
For a constant ππ ππ there is a point of maximum two-phase efficiency. This point occurs at an intake mixture flow
rate ππππ₯ ,πππ΅πΈπ higher than the surging flow rate ππππ₯ ππ£π
π π’πππππ.
0%
10%
20%
30%
40%
50%
60%
0% 10% 20% 30% 40% 50% 60%
Co
rre
lati
on
{ Ξ»
_in
@ S
urg
ing
}
Objective { Ξ»_in @ Surging }
Fitting Analysis: GVF at Intake Conditions for SurgingΞ»_sg = [ a1* (Qm_d) + a2*(Qm_d)^2 + a3*(Qm_d)^3] * (Ο^b0) * (Οg_avg/ΟL)^b1
Ο = 2600 rpm; P_in = 300 kPaΞ»_in = 10, 20, 30, 40, and 50 %
Ο = 3000 rpm; P_in = 300 kPaΞ»_in = 10, 20, 30, 40, and 50 %
Ο = 3600 rpm; P_in = 300 kPaΞ»_in = 5, 10, 15, 20, 25, 40, and 45 %
Ο = 3600 rpm; P_in = 100 kPaΞ»_in = 30%
Ο = 3600 rpm; P_in = 200 kPaΞ»_in = 30%
Ο = 3600 rpm; P_in = 300 kPaΞ»_in = 30%
Ο = 3600 rpm; P_in = 300 kPaΞ»_in = 30%
Reference Line
Reference Β± 10%
Reference Β± 20 %
0%
10%
20%
30%
40%
50%
60%
0 100 200 300 400 500 600 700 800
Ξ· [
% ]
-Tw
o-P
has
e E
ffic
ien
cy
Qmix [mΒ³/day] - Inlet Volumetric Flowrate
HGH Performance Test - Ο=3600 rpm - P1=300 kPa
Single Phase
Ξ»_inlet=5 %
Ξ»_inlet=10 %
Ξ»_inlet=15 %
Ξ»_inlet=20 %
Ξ»_inlet=25 %
Ξ»_inlet=30 %
Ξ»_inlet=40 %
Ξ»_inlet=45 %
Surging[ Max ΞP for Ξ»=cte ]
Two-PhaseIsothermal BEP
IV Journeys in Multiphase Flows (JEM 2015)
Additionally, as the ππ ππ increases, there is a reduction in the operational range limited by the open-flow and the
surging. The two-phase BEP occurs for an average mixture flow rate close to the single-phase BEP flow rate.
7. CONCLUSIONS
The bench tests of the 12-stage HGH using water and air evaluated the role of the following operational variables:
intake pressure πππ , rotation π, intake mixture flow rate ππππ₯,ππ, and either the intake gas volumetric fraction ππ ππ or
the intake gas volumetric flow rate ππ ππ.
The single-phase tests showed that the developed pressure Ξπ and the liquid flow rate ππΏ follow the affinity laws. It
was observed that the dimensionless BHP and the efficiency π depended on the rotation π, probably due to the torque
inaccuracy.
The two-phase head was calculated assuming that the two phases are in thermal equilibrium, that the gas is ideal
(π = 1) and considered an isothermal compression at an average temperature πππ£π between the intake πππ and the
outlet πππ’π‘ .
The two-phase tests showed that the equipment is able to pump mixtures with an intake gas volumetric fraction
ππ ππ up to 50 % with pressure gain and without surging. However, for high gas volumetric fractions ππ ππ, it was
observed a severe degradation in the developed pressure compared to the single-phase curve. There was also a
degradation in the two-phase efficiency. Additional tests are necessary to investigate the upper limit of the ππ ππ . The
operational range between the open-flow and the surging reduce as the intake gas volumetric fraction increases.
In the performance tests with constant ππ ππ , there was a reduction in the surging intake mixture flow rate ππππ₯ πππ π’πππππ
and an increase in the developed pressure Ξππ π’πππππ for a higher intake pressure πππ .
Normalized variables were used in order to compare the HGH performance at different rotations π. For a constant
intake pressure πππ and volumetric gas fraction ππ,ππ the normalized surging flow rate ππππ₯ πππ π’πππππ
decreased and the
normalized developed pressure Ξππ,π π’πππππ increased for a higher rotation π. Due to the higher pressure gain Ξπ there
was also a reduction in the outlet gas volumetric fraction ππ,ππ’π‘.
None of the two-phase dimensionless numbers Ξ π was constant at the surging points. More effort is required to
develop a surging correlation.
For a constant rotation π, intake pressure πππ , and gas volumetric pressure ππ,ππ the curves presented a point of two-
phase best efficiency. The inlet mixture flow rate at the two-phase BEP is higher than the surging flow rate for the same
intake conditions.
It is also necessary to investigate the effect of the HGH on an ESP installed downstream.
8. ACKNOWLEDGEMENTS
I would like to thank both Petrobras and Unicamp for sponsoring this work.
9. REFERENCES
Barrios, L. J., Visualization and Modeling of Multiphase Performance inside an Electrical Submersible Pump,
Dissertation, the University of Tulsa (2007)
Brown, K. E, Technology of Artificial Lift Methods, Vol 1b, Petroleum Publishing Co., Tulsa, Oklahoma (1980)
Estevam, V., A Phenomenological Analysis about Centrifugal Pump in Two-Phase Flow Operation, Ph.D Thesis,
Campinas: Faculdade de Engenharia MecΓ’nica, Universidade Estadual de Campinas (2002)
Gamboa, J., Prediction of the Transition in Two-Phase Performance of an Electrical Submersible Pump, Ph.D.
Dissertation, The University of Tulsa (2008)
Gulich, J. F., Centrifugal Pumps, Springer, Chapter 13 (2010)
Monte Verde, W., Experimental Investigation of Two-Phase Gas-Liquid Flow Performance of Electrical
Submersible Pump, Campinas: Faculdade de Engenharia MecΓ’nica, Universidade Estadual de Campinas (2011)
Pessoa, R. and Prado, M., , Two-Phase Flow Performance for Electric Submersible Pump Stages, SPE 71552,
(2001)
Romero, M., An Evaluation of an Electrical Submersible Pumping System for High GOR Wells, M.Sc Thesis, The
University of Tulsa (1999)
10. RESPONSIBILITY NOTICE
The author is the only responsible for the printed material included in this paper.