EXPERIMENTAL STUDY OF A MULTISTAGE HELICO-AXIAL GAS ...

IV Journeys in Multiphase Flows (JEM 2015) March 23-27, 2015, Campinas, SP, Brazil

Copyright © 2015 by ABCM Paper ID: JEM-2015-XXXX

EXPERIMENTAL STUDY OF A MULTISTAGE HELICO-AXIAL GAS

HANDLER OPERATING WITH WATER AND AIR

César Longhi Petrobras – International Technical Support – Rua do Senado, 20031 – 12th Floor – Rio de Janeiro – RJ – B razil

Unicamp – Mechanical Engineering – Energy Department – Rua Mendeleyev, 200 – Campinas – SP – Brazil

[email protected]

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 – Cepetro – 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 – 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 – 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 – Best

Efficiency Point. These tests usually employ water as working fluid and accomplish the API – American Petroleum

Institute – 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 𝜆𝑔 in a cross sectional area, such as the pump intake or outlet, is defined as the ratio

between the in situ gas 𝑄𝑔 and the mixture 𝑄𝑚𝑖𝑥 volumetric flow rates and given by Equation 1

𝜆𝑔 = 𝑄𝑔

𝑄𝑚𝑖𝑥

( 1 )

mailto:[email protected]

César Longhi Experimental Study of a Multistage Helico-Axial Gas Handler operating with Water and Air

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The definition of 𝜆𝑔 is based on the in situ volumetric flow rates through a cross area. It differs from the definition

of the gas hold up 𝛼𝑔, which is the ratio between the in situ volumes occupied by the gas 𝒱𝑔 and the mixture 𝒱𝑚𝑖𝑥 in a

control volume, expressed by the following equation.

𝛼𝑔 = 𝒱𝑔

𝒱𝑚𝑖𝑥

( 2 )

The ESP performance tends to degrade due to the gas phase. For low gas volumetric fractions 𝜆𝑔 and high liquid

flow rates 𝑄𝐿 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 𝜔, fluid properties (composition,

pressure and temperature), flow rate of each phase (or equivalently the mixture flow rate 𝑄𝑚𝑖𝑥 and the gas volumetric

fraction 𝜆𝑔) , and flow pattern parameters at the pump intake (e.g. stochastic distribution of the bubble diameter 𝑑𝐵).

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 𝑃𝑖𝑛 and the intake gas volumetric fraction 𝜆𝑔,𝑖𝑛 are kept constant,

while the liquid flow rate is reduced. The surging condition corresponds to the maximum developed pressure ∆𝑃, given

by Eq. ( 3 ):

(𝜕 ∆𝑃

𝜕𝑄𝑚𝑖𝑥,𝑖𝑛)

𝜆𝑖𝑛=𝑐𝑡𝑒𝑃𝑖𝑛=𝑐𝑡𝑒

𝑆𝑢𝑟𝑔𝑖𝑛𝑔

= 0 ( 3 )

The surging phenomenon is related to system instabilities when the pump operates in a region where the

performance curve has a positive ∆𝑃(𝑄) 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.

IV Journeys in Multiphase Flows (JEM 2015)

Commercial gas handlers can have different physical principles and geometries. The gas handler performance

curves also tend to degrade for increasing gas volumetric fractions 𝜆𝑔, but less severely than for an ESP. On the other

hand, for single-phase or very low gas volumetric fraction 𝜆𝑔, the ESP can be more efficient than the gas handler.

2.1 AGH – Advanced Gas Handler

The Reda AGH – Advanced Gas Handler – 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 – 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 ��𝑚𝑒𝑐 (also known as BHP – brake horse power) and the single-phase hydraulic power ��ℎ𝑦𝑑

for a pump (ESP or HGH) are given by Eq. ( 4 ) and Eq. ( 5 ):

��𝑚𝑒𝑐 = 𝜔 𝜏𝑠ℎ𝑎𝑓𝑡

( 4 )

��ℎ𝑦𝑑 = 𝑄𝐿 Δ𝑃 ( 5 )

where 𝑄𝐿 is the liquid flow rate, Δ𝑃 is the developed pressure, 𝜔 is the rotation, and 𝜏𝑠ℎ𝑎𝑓𝑡 is the shaft torque.

The single-phase efficiency 𝜂 is defined as the ratio between the hydraulic and the mechanical power, given by:

𝜂 =��ℎ𝑦𝑑

��𝑚𝑒𝑐

( 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 𝜌, the rotation 𝜔, and the rotor diameter 𝐷𝑝 . The dependent

variables were the liquid flow rate 𝑄𝐿 , the developed pressure Δ𝑃, the mechanical power ��𝑚𝑒𝑐 , the viscosity 𝜇, the


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geometrical parameters 𝐿𝑖 of the pump, and the superficial roughness 𝑒. Table 1shows the dimensionless numbers

obtained:

Table 1- Dimensionless Numbers for Single Phase Pumping

Specific Capacity 𝑄𝐿

∗ = 𝑄𝐿

𝜔 𝐷𝑝3

( 7 )

Specific Developed Pressure Δ𝑃∗ =

Δ𝑃

𝜌 𝜔2 𝐷𝑝2

( 8 )

Specific Mechanical Power ��𝑚𝑒𝑐

∗ =��𝑚𝑒𝑐

𝜌 𝜔3 𝐷𝑝5

( 9 )

Reynolds Number 𝑅𝑒 =

𝜌𝜔𝐷𝑝2

𝜇

( 10 )

Geometry Dimensionless Numbers 𝐿𝑖

∗ = 𝐿𝑖

𝐷𝑝

( 11 )

Relative Roughness 휀 = 𝑒

𝐷𝑝

( 12 )

The torque 𝜏 and the mechanical power ��𝑚𝑒𝑐 are related to each other by the rotation 𝜔, which is an independent

variable of the dimensional analysis, resulting in the same dimensionless number.

During the tests the dimensionless geometry numbers 𝐿𝑖∗ were kept constant. The variation of the superficial

roughness 𝑒 due to aging is assumed to be negligible. It is observed that for a single-phase low viscosity liquid the

Reynolds number 𝑅𝑒 does not play a relevant role. Therefore, for a given pump the specific head Δ𝑃∗ and the specific

brake horsepower ��𝑚𝑒𝑐∗ can expressed as functions of only the specific capacity 𝑄𝐿

∗.

The developed pressure Δ𝑃 is directly proportional to the specific mass 𝜌. Defining a reference gravity acceleration

𝑔, the single-phase developed head 𝐻 is defined by Eq. ( 13 ):

𝐻 =Δ𝑃

𝑔 𝜌

( 13 )

The single-phase efficiency 𝜂 can be expressed in terms of the dimensionless numbers as:

𝜂 =𝑄𝐿

∗ Δ𝑃∗

��𝑚𝑒𝑐∗

( 14 )

The primary dimensionless numbers specific capacity 𝑄𝐿∗ and specific developed pressure Δ𝑃∗ can be combined to

generate the specific speed 𝑁∗, a dimensionless number independent of the rotor diameter 𝐷𝑝 and with a unitary

rotation 𝜔 exponent, given by Eq. ( 15 ):

𝑁∗ =(𝑄𝐿

∗)12

(Δ𝑃∗ )34

=𝜔 𝑄𝐿

12

(𝑔𝐻)34

( 15 )

The specific speed 𝑁∗ is usually defined at the BEP – 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 𝑄𝐿𝑑 is defined by Eq. ( 16 ) as the ratio between the liquid flow

rate 𝑄𝐿 and the maximum flow rate 𝑄𝑠𝑖𝑛𝑔𝑙𝑒−𝑝ℎ𝑎𝑠𝑒𝑜𝑝𝑒𝑛−𝑓𝑙𝑜𝑤

at the same rotation 𝜔:

𝑄𝐿𝑑 = 𝑄𝐿

𝑄𝑠𝑖𝑛𝑔𝑙𝑒−𝑝ℎ𝑎𝑠𝑒𝑜𝑝𝑒𝑛−𝑓𝑙𝑜𝑤

( 16 )


If the liquid specific mass 𝜌 is constant, the normalized pressure Δ𝑃𝑑 is defined by Eq. ( 17 ) as the ratio between

the developed pressure Δ𝑃 and the shut-in pressure Δ𝑃𝑠𝑖𝑛𝑔𝑙𝑒−𝑝ℎ𝑎𝑠𝑒𝑠ℎ𝑢𝑡−𝑖𝑛 at the same rotation 𝜔.

Δ𝑃𝑑 = Δ𝑃

Δ𝑃𝑠𝑖𝑛𝑔𝑙𝑒−𝑝ℎ𝑎𝑠𝑒𝑠ℎ𝑢𝑡−𝑖𝑛 for 𝜌 = 𝑐𝑡𝑒 ( 17 )

If there is a change in the liquid specific mass 𝜌, it is more convenient to define a normalized head H𝑑 according to

Eq. ( 18 ):

H𝑑 = H

H𝑠𝑖𝑛𝑔𝑙𝑒−𝑝ℎ𝑎𝑠𝑒𝑠ℎ𝑢𝑡−𝑖𝑛

( 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 ):

𝑄𝑚𝑖𝑥 = 𝑄𝐿 + 𝑄𝑔

( 19 )

��𝑚𝑖𝑥 = ��𝐿 + ��𝑔 ( 20 )

The gas mass fraction 𝜒𝑔 is defined as the ratio between the gas and the mixture mass flow rates, given by ( 21 ):

𝜒𝑔 = ��𝑔

��𝑚𝑖𝑥

( 21 )

The massic �� and the volumetric 𝑄 flow rates of each phase are related to the specific mass 𝜌 by:

��𝑔 = 𝜌𝑔𝑄𝑔

( 22 )

��𝐿 = 𝜌𝐿𝑄𝐿 ( 23 )

The liquid specific mass 𝜌𝐿 is assumed to be constant (incompressible fluid, no thermal dilatation), whilst the gas

specific mass 𝜌𝑔 is given by Eq. ( 24 ):

𝜌𝑔 =𝑀𝑎𝑣𝑔 𝑃𝑎𝑏𝑠

ℜ𝑢 𝑍 𝑇𝑎𝑏𝑠

( 24 )

where: 𝜌𝑔 is the gas specific mass, 𝑀𝑎𝑣𝑔 is the average molecular weight of the gas, ℜ𝑢 is the gas universal

constant, 𝑍 is the gas compressibility factor, 𝑃𝑎𝑏𝑠 is the absolute pressure, and 𝑇𝑎𝑏𝑠 is the absolute temperature.

For the gas flow rate 𝑄𝑔, the mixture flow rates 𝑄𝑚𝑖𝑥, and the gas volumetric fraction 𝜆𝑔 it is necessary to specify

the thermodynamic condition considered (pressure 𝑃 and temperature 𝑇). The average thermodynamic conditions

between the intake and the outlet are defined by Eq. ( 25 ) and Eq. ( 26 ):

𝑇𝑎𝑣𝑔 =𝑇𝑖𝑛 + 𝑇𝑜𝑢𝑡

2

( 25 )

𝑃𝑎𝑣𝑔 =𝑃𝑖𝑛 + 𝑃𝑜𝑢𝑡

2

( 26 )

where the subscripts have the following meanings: 𝑖𝑛 for intke, 𝑜𝑢𝑡 for outlet, and 𝑎𝑣𝑔 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 𝜆𝑔 < 80%. The


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thermodynamic process is approximated by an isothermal compression at the average temperature 𝑇𝑎𝑣𝑔 between the

intake 𝑇𝑖𝑛 and the outlet 𝑇𝑜𝑢𝑡 .

The power delivered to a mixture ��𝑚𝑖𝑥 is assumed to be equal to the sum of the power delivered to the liquid and

to the gas phases according to Eq. ( 27 ):

��𝑚𝑖𝑥 = ��𝐿 + ��𝑔 ( 27 )

As the head 𝐻 represents the increment of the fluid specific energy in terms of an equivalent elevation in a

reference gravitational field 𝑔, the power delivered to each phase is given by Eq. ( 28 ) and Eq. ( 29 ):

��𝐿 = ��𝐿 𝑔 𝐻𝐿

( 28 )

��𝑔 = ��𝑔 𝑔 𝐻𝑔 ( 29 )

In Eq. ( 28 ) and Eq. ( 29 ) the mass flow rates ��𝐿 and ��𝑔 are constant. The equivalent head of each phase,

represented by 𝐻𝑝ℎ𝑎𝑠𝑒 , is given by Eq. ( 30 ):

𝐻𝑝ℎ𝑎𝑠𝑒 =1

𝑔∫

𝛿𝑃

𝜌𝑝ℎ𝑎𝑠𝑒

𝑃𝑜𝑢𝑡

𝑃𝑖𝑛

( 30 )

The symbol 𝛿𝑃 indicates that the integral depends not only on the integration limits 𝑃𝑖𝑛 and 𝑃𝑜𝑢𝑡 but also on the

thermodynamic process, since 𝜌𝑝ℎ𝑎𝑠𝑒 is a function of both the pressure 𝑃 and the temperature 𝑇. Assuming that liquid

phase is incompressible (𝜌𝐿 = 𝑐𝑡𝑒), the liquid head 𝐻𝐿 is given by Eq. ( 31 ):

𝐻𝐿 = 𝑃𝑜𝑢𝑡 − 𝑃𝑖𝑛

𝑔 𝜌𝐿

( 31 )

Assuming that the gas is ideal (𝑍 = 1), the gas phase isothermal head is given by:

𝐻𝑔

𝑇=𝑇𝑎𝑣𝑔 =

ℜ𝑢 𝑇𝑎𝑣𝑔𝑎𝑏𝑠

𝑔 𝑀𝑔

𝑙𝑛 (𝑃𝑜𝑢𝑡

𝑎𝑏𝑠

𝑃𝑖𝑛𝑎𝑏𝑠 )

( 32 )

The two-phase isothermal head 𝐻𝑚𝑖𝑥

𝑇=𝑇𝑎𝑣𝑔 is defined as:

𝐻𝑚𝑖𝑥

𝑇=𝑇𝑎𝑣𝑔=

��𝑚𝑖𝑥

𝑇=𝑇𝑎𝑣𝑔

��𝑚𝑖𝑥 𝑔=

��𝐿 𝑔 𝐻𝐿 + ��𝑔 𝑔 𝐻𝑔


��𝑚𝑖𝑥 𝑔

( 33 )

Substituting Eq. ( 21 ) in Eq. ( 33 ) it is obtained Eq. ( 34 ):

𝐻𝑚𝑖𝑥

𝑇=𝑇𝑎𝑣𝑔= (1 − 𝜒𝑔)𝐻𝐿 + 𝜒𝑔𝐻𝑔

𝑇=𝑇𝑎𝑣𝑔 ( 34 )

The two-phase isothermal efficiency 𝜂 is defined by Eq. ( 35 ):

𝜂 =��

𝑚𝑖𝑥


��𝑚𝑒𝑐

( 35 )

4.2 Dimensionless Numbers for Two-Phase Pumping

The developed pressure Δ𝑃 for a two-phase mixture is a function of the variables shown in Eq. ( 36 ) (Gamboa,

2008):

Δ𝑃𝐺𝑎𝑚𝑏𝑜𝑎 = 𝑓(𝜌𝐿 , 𝜌𝑔 , 𝜇𝐿 , 𝜇𝑔 , 𝜎, 𝜔, 𝑔, 𝑄𝐿 , 𝑄𝑔 , 𝐷𝑝) ( 36 )

where 𝜎 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 𝜃 to the horizontal, the superficial roughness 𝑒 and the geometrical

parameters 𝐿𝑖 of the pump and the bench (e.g. nozzle diameters for gas injection, pipe diameter, etc), which might


affect the stochastic distribution of the flow pattern parameters. Besides the developed pressure Δ𝑃 it might be of

interest the mechanical power W𝑚𝑒𝑐, also known as brake horse-power. Thus:

ΔP = 𝑓(𝜌𝐿 , 𝜌𝑔 , 𝜇𝐿 , 𝜇𝑔 , 𝜎, 𝜔, 𝑔, 𝑄𝐿 , 𝑄𝑔 , 𝐷𝑝 , 𝜃, 𝑒, 𝐿𝑖)

( 37 )

��𝑚𝑒𝑐 = 𝑓(𝜌𝐿 , 𝜌𝑔 , 𝜇𝐿 , 𝜇𝑔 , 𝜎, 𝜔, 𝑔, 𝑄𝐿 , 𝑄𝑔 , 𝐷𝑝 , 𝜃, 𝑒, 𝐿𝑖) ( 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 𝜌𝐿 , the rotation 𝜔, and the rotor diameter 𝐷𝑝 as independent variables and

applying the Buckingham Pi theorem, the dimensionless numbers governing the problem are shown in Table 2:

Table 2 – Dimensionless Numbers for Two-Phase Pumping

Specific Developed Pressure Π1,𝑎 = Δ𝑃∗ = Δ𝑃

𝜌 𝜔2 𝐷𝑝2 ( 39 )

Specific Mechanical Power Π1,𝑏 = ��𝑚𝑒𝑐∗ =

��𝑚𝑒𝑐

𝜌 𝜔3 𝐷𝑝5 ( 40 )

Gas to Liquid Specific Mass Ratio Π2 =𝜌𝑔

𝜌𝐿

( 41 )

Reynolds Number for the Liquid Phase Π3 =𝜇𝐿

𝜌𝐿 𝜔 𝐷𝑝2

=1

𝑅𝑒𝐿

( 42 )

Dimensionless Gas Viscosity Π4 =𝜇𝑔

𝜌𝐿 𝜔 𝐷𝑝2

=𝜇𝑔

𝜇𝐿 𝑅𝑒𝐿 ( 43 )

Dimensionless Interfacial Tension Π5 = 𝜎∗ = 𝜎

𝜌 𝜔2 𝐷𝑝3 ( 44 )

Specific Gravitational Acceleration Π6 = 𝑔∗ = 𝑔

𝜔2 𝐷𝑝

( 45 )

Specific Liquid Capacity Π7 = 𝑄𝐿∗ =

𝑄𝐿

𝜔 𝐷𝑝3 ( 46 )

Specific Gas Capacity Π8 = 𝑄𝑔∗ =

𝑄𝑔

𝜔 𝐷𝑝3 ( 47 )

Inclination to Horizontal Π9 = 𝜃 ( 48 )

Specific Roughness Π10 = 휀 = 𝑒

𝐷𝑝

( 49 )

Dimensionless Geometric Parameters Π11,𝑖 = 𝐿𝑖∗ =

𝐿𝑖

𝐷𝑝

( 50 )

The dimensionless numbers 𝑄𝐿∗ and 𝑄𝑔

∗ can be combined into the dimensionless numbers shown in Eq. ( 51 ) and

Eq. ( 52 ):

𝑄𝑚𝑖𝑥∗ = 𝑄𝐿

∗ + 𝑄𝑔∗

( 51 )

𝜆𝑔 =𝑄𝑔

∗

𝑄𝑚𝑖𝑥∗

( 52 )

where 𝑄𝑚𝑖𝑥∗ is the specific mixture capacity and 𝜆𝑔 is the gas volumetric fraction.


8

4.3 Two-Phase Normalization

The two-phase normalized flow rates (liquid 𝑄𝐿𝑑, gas 𝑄𝑔𝑑 or mixture 𝑄𝑚𝑖𝑥 𝑑) and the normalized developed

pressure Δ𝑃𝑑 are defined by Eq. ( 53 ) and Eq. ( 54 ):

𝑄𝑑 = 𝑄

𝑄𝑠𝑖𝑛𝑔𝑙𝑒−𝑝ℎ𝑎𝑠𝑒𝑜𝑝𝑒𝑛−𝑓𝑙𝑜𝑤

( 53 )

Δ𝑃𝑑 = Δ𝑃

Δ𝑃𝑠𝑖𝑛𝑔𝑙𝑒−𝑝ℎ𝑎𝑠𝑒𝑠ℎ𝑢𝑡−𝑖𝑛

( 54 )

The gas volumetric fraction 𝜆𝑔 is directly given by Eq.( 55 ) involving the normalized flow rates:

𝜆𝑔 = 𝑄𝑔 𝑑

𝑄𝑚𝑖𝑥 𝑑

( 55 )

5. EXPERIMENTAL TESTS

The HGH water-air tests have been carried out in a horizontal bench at Unicamp – Cepetro – Labpetro. This bench

was used by Monte Verde (2011) to test the AGH.

5.1 Test Facilities

The HGH rotation 𝜔, constant for each curve, was set on the panel of a VSD – 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 𝜙𝑔 of the air valve

and the rotation 𝜔𝑏 of the liquid booster were controlled via software. The pressure 𝑃𝑔 upstream the gas valve was set

manually with two gas pressure regulators in tandem. The opening 𝜙𝑚 of the valve installed downstream the HGH was

manually operated. The control variables are summarized in Table 3.

Table 3 – Control Variables

Variable Description Control

𝜔 HGH Rotation VSD Pannel

𝜔𝑏 Booster Booster-VSD via software

𝑃𝑔 Pressure upstream the gas valve Two manual regulators in Tandem

𝜙𝑔 Opening of the gas valve Via software

𝜙𝑚 Valve upstream the HGH Manual

The variables measured by the software are shown in Table 4:

Table 4 – Measured Variables

Variable Description Sensor

𝑇𝑖𝑛 Liquid temperature at the HGH inlet PT100

𝑇𝑜𝑢𝑡 Mixture temperature at the HGH outlet PT100

𝑃𝑖𝑛 HGH Intake pressure Rosemount

𝑃𝑜𝑢𝑡 HGH Outlet pressure Rosemount

𝑃𝑔 Pressure upstream the gas valve Rosenount

��𝐿 Liquid mass flow rate Coriolis

��𝑔 Gas mass flow rate Coriolis

𝜏𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 Measured Torque Torquemeter


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 ):

𝜏𝑠ℎ𝑎𝑓𝑡_𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 = 𝜏𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 − 𝜏𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙 ( 56 )

where: 𝜏𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 is the measured torque, 𝜏𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙 is the residual torque (no mechanical load), and 𝜏𝑠ℎ𝑎𝑓𝑡_𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑

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 𝜔, the axial load 𝐹𝑎𝑥𝑖𝑎𝑙 , and the temperature 𝑇𝑙𝑢𝑏 of the lubrication fluid. The effect of

the axial load is neglected. It is assumed that the temperature of the lubrication fluid 𝑇𝑙𝑢𝑏 depends basically upon the

rotation. The HGH corrected shaft torque 𝜏𝑠ℎ𝑎𝑓𝑡_𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 is used to calculate the average torque per stage 𝜏𝑠𝑡𝑔

according to Eq. ( 57 ):

𝜏𝑠𝑡𝑔 = 𝜏𝑠ℎ𝑎𝑓𝑡_𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑

𝑛𝑠𝑡𝑔

( 57 )

where: 𝜏𝑠𝑡𝑔 is the average torque per stage and 𝑛𝑠𝑡𝑔 is the number of stages.

5.4 Single-Phase Tests

For the single-phase tests there is no gas injection (𝑄𝑔 = 0; 𝜆𝑔 = 0) and the intake pressure 𝑃𝑖𝑛 does not have

to be controlled, providing the bench operational constraints are respected. The liquid flow rate 𝑄𝐿 ranged from slightly

above the open-flow (Δ𝑃 = 0) to the shut-in (𝑄𝐿 = 0) condition.

5.5 Two-Phase Test Procedure

The performance tests consist in decreasing the liquid flow rate 𝑄𝐿 for a constant rotation 𝜔, intake pressure 𝑃𝑖𝑛

and either gas volumetric flow rate 𝑄𝑔,𝑖𝑛 or the gas volumetric fraction 𝜆𝑔,𝑖𝑛 at the HGH intake.

For each curve the inlet mixture flow rate 𝑄𝑚𝑖𝑥,𝑖𝑛 started slightly above the open-flow (no developed pressure) and

was reduced until an unstable condition was reached. The inlet mixture flow rate 𝑄𝑚𝑖𝑥,𝑖𝑛 was reduced by closing the

manual valve 𝜙𝑚 downstream the HGH. Then the rotation 𝜔𝑏 of the VSD liquid booster, the gas valve opening 𝜙𝑔

and/or the regulated gas pressure 𝑃𝑔 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).


10

Figure 2 – Residual torque

6.2 Single-Phase Tests

The single-phase tests using water as working fluid were performed at 𝜔 = 2100, 2600, 3000, and 3600 rpm. The

manufacturer reference curves are not presented due to the confidentiality agreement.

Figure 3 – 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 – Average developed pressure and corrected average torque per stage for single-phase tests

y = 9.81409E-08x2 - 1.22493E-05x + 7.12870E-01R² = 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

ΔP

[ k

Pa

] -

Pre

ssu

re In

cre

me

nt

QL [m³/day] - Liquid Flowrate

HGH Single Phase

ω=3600 rpm

ω=3000 rpm

ω=2600 rpm

ω=2100 rpm

0

5

10

15

20

25

0 100 200 300 400 500 600 700 800

τ_m

eas

ure

d [

N.m

] -

Me

asu

red

To

rqu

e


HGH Single Phase

ω=3600 rpm

ω=3000 rpm

ω=2600 rpm

ω=2100 rpm

-40

-20

0

20

40

60

80

100

120

0 100 200 300 400 500 600 700 800

ΔP

[ k

Pa/

stag

e ]

-A

vera

ge P

ress

ure

Incr

em

en

t p

er

Stag

e


HGH Single Phase

ω=3600 rpm

ω=3000 rpm

ω=2600 rpm

ω=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

τ_st

g [N

.m]

-A

vega

re T

orq

ue

pe

r St

age


HGH Single Phase

ω=3600 rpm

ω=3000 rpm

ω=2600 rpm

ω=2100 rpm


Figure 5 – 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 𝑄𝐿∗, ∆𝑃∗ ,

��𝑚𝑒𝑐∗ , 𝑁∗ , and the efficiency 𝜂:

Figure 6 – 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 ∆𝑃∗(𝑄𝐿∗) plots for the different rotations 𝜔, the effect of the Reynolds

number 𝑅𝑒 seems to be negligible. The differences in the specific brake horsepower ��𝑚𝑒𝑐∗ and efficiency 𝜂 might have

been caused by the torque inaccuracy.

The following figures show the single-phase test results expressed in terms of normalized flow rate 𝑄𝐿 𝑑,

normalized pressure ∆𝑃𝑑 and efficiency 𝜂:

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600 700 800

Ẇ_m

ec_

stg

[ W

att/

stg

] -

Ave

rage

BH

P M

ech

anic

al

Po

we

r p

er

HG

H-S

tage


HGH Single Phase

ω=3600 rpm

ω=3000 rpm

ω=2600 rpm

ω=2100 rpm

0%

10%

20%

30%

40%

50%

60%

0 100 200 300 400 500 600 700 800

η [

% ]

-Ef

fici

en

cy


HGH Single Phase

ω=3600 rpm

ω=3000 rpm

ω=2600 rpm

ω=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

ΔP

* -

Spe

cifi

c H

ead

pe

r St

age

QL* - Specific Liquid Capacity

HGH Single Phase

ω=3600 rpm

ω=3000 rpm

ω=2600 rpm

ω=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

Ẇ_m

ec*

-Sp

eci

fic

Bre

ak H

ors

ep

ow

er

pe

r St

age


HGH Single Phase

ω=3600 rpm

ω=3000 rpm

ω=2600 rpm

ω=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

η [

% ]

-Ef

fici

en

cy


HGH Single Phase

ω=3600 rpm

ω=3000 rpm

ω=2600 rpm

ω=2100 rpm

0%

10%

20%

30%

40%

50%

60%

1.0E-01 1.0E+00 1.0E+01 1.0E+02

η [

% ]

-Ef

fici

en

cy

N* - Specific Speed

HGH Single Phase

ω=3600 rpm

ω=3000 rpm

ω=2600 rpm

ω=2100 rpm


12

Figure 7 – 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 𝑄𝑔,𝑖𝑛 = 𝑐𝑡𝑒 obtained at three different rotations (𝜔 =

2600 rpm, 3000 rpm, and 3600 rpm) for the same intake pressure 𝑃𝑖𝑛 = 300 𝑘𝑃𝑎.

Figure 8 – 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 𝑄𝑔 and high liquid 𝑄𝐿 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

(ΔP/

ΔP

_sp

_max

) -

No

rmal

ize

d P

ress

ure

(QL/Qmax) - Normalized Liquid Flowrate

HGH Single Phase

ω=3600 rpm

ω=3000 rpm

ω=2600 rpm

ω=2100 rpm

BEP @ ω = 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

η [

% ]

-Ef

fici

en

cy

(QL/Qmax) - Normalized Liquid Flowrate

HGH Single Phase

ω=3600 rpm ω=3000 rpm ω=2600 rpm ω=2100 rpm BEP @ ω = 3600 rpm

0

10

20

30

40

50

60

0 50 100 150 200 250 300 350 400 450 500

ΔP

[ k

Pa/

stag

e ]

-A

vera

ge P

ress

ure

Incr

em

en

t p

er

Stag

e

Qmix_in [m³/day] - Intake Volumetric Mixture Flowrate

HGH Performance Test - ω = 2600 rpm - P_in=300 kPa - Qg_in=cte

Single Phase

Qg_in=24.6 m³/day

Qg_in=49.54 m³/day

Qg_in=74.39 m³/day

0

10

20

30

40

50

60

70

80

0 100 200 300 400 500 600

ΔP

[ k

Pa/

stag

e ]

-A

vera

ge P

ress

ure

Incr

em

en

t p

er

Stag

e



Single Phase

Qg_in=28.3 m³/day

Qg_in=57.2 m³/day

Qg_in=85.8 m³/day

0

20

40

60

80

100

120

0 100 200 300 400 500 600 700

ΔP

[ k

Pa/

stag

e ]

-A

vera

ge P

ress

ure

Incr

em

en

t p

er

Stag

e



Single Phase

Qg_in=17 m³/day

Qg_in=34 m³/day

Qg_in=51.5 m³/day

Qg_in=68.6 m³/day

Qg_in=90 m³/day

Qg_in=103 m³/day

Qg_in=128.6 m³/day


higher gas flow rates 𝑄𝑔. For low liquid flow rates 𝑄𝐿 the system became unstable even for moderate gas flow rates 𝑄𝑔.

No gas lock was observed.

Effect of the Rotation 𝝎 for 𝑸𝒈,𝒊𝒏 = 𝒄𝒕𝒆

The three curves in the following figure have the same normalized gas volumetric flow rate 𝑄𝑔 𝑖𝑛,𝑑 = 0.1568 at the

HGH intake:

Figure 9 – Effect of the rotation on the average developed pressure for a constant intake pressure 300 kPa and

normalized gas flow rate 𝑄𝑔𝑑,𝑖𝑛 = 0.1568

The effect of the rotation 𝜔 is evaluated by expressing the data in terms of the normalized mixture flow rate 𝑄𝑚𝑖𝑥 𝑑

and the normalized developed pressure Δ𝑃𝑑:

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 𝑄𝑔𝑑,𝑖𝑛 = 0.1568

If the mixture flow rate is below the open-flow (positive pressure gain condition), a higher rotation 𝜔 is associated

with a lower gas volumetric fraction 𝜆𝑔,𝑜𝑢𝑡 at the outlet and with a higher normalized pressure Δ𝑃𝑑. As the normalized

gas volumetric flow rate 𝑄𝑔 𝑖𝑛,𝑑 at the inlet is constant for each curve, the inlet gas volumetric fraction 𝜆𝑔,𝑖𝑛 decreases

monotonically with the normalized mixture flow rate 𝑄𝑚𝑖𝑥 𝑖𝑛,𝑑. The outlet 𝜆𝑔,𝑜𝑢𝑡 and the intake 𝜆𝑔,𝑖𝑛 gas volumetric

fractions are equal for the open-flow condition. No effect of the rotation 𝜔 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 (𝑃𝑖𝑛 = 300 𝑘𝑃𝑎) varying the intake gas

volumetric fraction 𝜆𝑔 𝑖𝑛 for three different rotations (𝜔 = 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

ΔP

[ k

Pa/

stag

e ]

-A

vera

ge P

ress

ure

Incr

em

en

t p

er

Stag

e


HGH Performance Test - P_in=300 kPa - Qg_in_d=0.1568

ω=2600 rpm - Qg_in=74.39 m³/day

ω=3000 rpm - Qg_in=85.8 m³/day

ω=3600 rpm - Qg_in=103 m³/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

(ΔP/

ΔP

_sp

_max

) -

No

rmal

ize

d P

ress

ure

(Qmix_in/Q_sp_max) - Normalized Inlet Mixture Flowrate


Single Phase

ω=2600 rpm - Qg_in=74.39 m³/day

ω=3000 rpm - Qg_in=85.8 m³/day

ω=3600 rpm - Qg_in=103 m³/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

λ_o

ut

[ %

] -

Ou

tlet

GV

F

λ_in

[ %

] -

Inle

t G

VF



λ_in [ % ] - ω=2600 rpm - Qg_in=74.39 m³/day λ_in [ % ] - ω=3000 rpm - Qg_in=85.8 m³/day

λ_in [ % ] - ω=3600 rpm - Qg_in=103 m³/day λ_out [ % ] - ω=2600 rpm - Qg_in=74.39 m³/day

λ_out [ % ] - ω=3000 rpm - Qg_in=85.8 m³/day λ_out [ % ] - ω=3600 rpm - Qg_in=103 m³/day


14

Figure 11 – 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 𝜆𝑔 𝑖𝑛 increases, the surging point occurs at a

higher inlet mixture flow rate 𝑄𝑚𝑖𝑥 𝑖𝑛𝑠𝑢𝑟𝑔𝑖𝑛𝑔

and corresponds to a lower developed pressure Δ𝑃𝑠𝑢𝑟𝑔𝑖𝑛𝑔. For a higher gas

volumetric fraction 𝜆𝑔,𝑖𝑛 at the intake there was also a reduction in the inlet mixture flow rate in the open-flow

condition, represented by 𝑄𝑚𝑖𝑥 𝑖𝑛𝑜𝑝𝑒𝑛−𝑓𝑙𝑜𝑤

.

Effect of the Intake Pressure 𝑷𝒊𝒏 for 𝝎 = 𝟑𝟎𝟎𝟎 𝒓𝒑𝒎 and 𝝀𝒈,𝒊𝒏 = 𝟑𝟎%

The following figure shows the effect of the intake pressure 𝑃𝑖𝑛 for 𝜔 = 3600 𝑟𝑝𝑚 and 𝜆𝑖𝑛 = 30%:

Figure 12 – 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

ΔP

[ k

Pa/

stag

e ]

-A

vera

ge P

ress

ure

Incr

em

en

t p

er

Stag

e


HGH Performance Test - ω = 2600 rpm - P_in=300 kPa - λ_in=cte

Single Phase

λ_in=10 %

λ_in=20 %

λ_in=30 %

λ_in=40 %

λ_in=50 %

0

10

20

30

40

50

60

70

80

0 100 200 300 400 500 600

ΔP

[ k

Pa/

stag

e ]

-A

vera

ge P

ress

ure

Incr

em

en

t p

er

Stag

e



Single Phase

λ_in=10 %

λ_in=20 %

λ_in=30 %

λ_in=40 %

λ_in=50 %

0

20

40

60

80

100

120

0 100 200 300 400 500 600 700

ΔP

[ k

Pa/

stag

e ]

-A

vera

ge P

ress

ure

Incr

em

en

t p

er

Stag

e



Single Phase

λ_in=5 %

λ_in=10 %

λ_in=20 %

λ_in=30 %

λ_in=40 %

λ_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

(ρg_

avg

/ρL)

-G

as-L

iqu

id ρ

Rat

io a

t A

vera

ge

The

rmo

dyn

amic

Co

nd

itio

ns


HGH Performance Test - ω = 3600 rpm - λ_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

λ_o

ut

[ %

] -

Ou

tlet

GV

F



P_in=100 kPa

P_in=200 kPa

P_in=300 kPa



Figure 13 - Effect of the intake pressure on the average developed pressure

The curve with 𝑃𝑖𝑛 = 400 𝑘𝑃𝑎 could not reach higher flow rates due to limitations in the gas injection. The

developed pressure Δ𝑃 curves are similar, although the surging point occurred at lower mixture flow rates 𝑄𝑚𝑖𝑥 𝑖𝑛𝑠𝑢𝑟𝑖𝑛𝑔

for

higher intake pressures 𝑃𝑖𝑛 . If the mixture flow rate is below the open-flow (positive pressure gain condition), a higher

intake pressure 𝑃𝑖𝑛 corresponds to a lower gas volumetric fraction 𝜆𝑜𝑢𝑡 at the outlet. It also corresponds to a higher

average gas to liquid specific mass ratio, represented by (𝜌𝑔,𝑎𝑣𝑔

𝜌𝐿⁄ ).

Effect of the Rotation 𝝎 for 𝑷𝒊𝒏 = 𝟑𝟎𝟎 𝒌𝑷𝒂 and 𝝀𝒈,𝒊𝒏 = 𝟏𝟎%

Figure 14 shows that for high mixture flow rates and low intake gas volumetric fractions (𝜆𝑔,𝑖𝑛 = 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 – 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

ΔP

[ k

Pa/

stag

e ]

-A

vera

ge P

ress

ure

Incr

em

en

t p

er

Stag

e



Single Phase

P_in=100 kPa

P_in=200 kPa

P_in=300 kPa


-40

-20

0

20

40

60

80

100

120

0 100 200 300 400 500 600 700 800

ΔP

[ k

Pa/

stag

e ]

-A

vera

ge P

ress

ure

Incr

em

en

t p

er

Stag

e

Qmix [m³/day] - Inlet Volumetric Flowrate

HGH Performance Test - P1=300 kPa - λ_inlet=10 %

Single Phase ω=3600 rpm



ω=3600 rpm - λ_inlet=10 %



Surging [Max ΔP for λ_in=cte; P_in=cte]


16

Figure 15 – 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 𝝎 for 𝑷𝒊𝒏 = 𝟑𝟎𝟎 𝒌𝑷𝒂 and 𝝀𝒈,𝒊𝒏 = 𝟑𝟎%

The following figures show the normalized developed pressure Δ𝑃𝑑 and the outlet gas volumetric fraction 𝜆𝑔,𝑜𝑢𝑡 as

a function of the normalized mixture intake flow rate 𝑄𝑚𝑖𝑥 𝑖𝑛,𝑑 for 𝑃𝑖𝑛 = 300 𝑘𝑃𝑎 and 𝜆𝑔,𝑖𝑛 = 30% at three different

rotations (𝜔 = 2600, 3000, and 3600 rpm).

Figure 16 – 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 𝜆𝑔,𝑜𝑢𝑡 decreases and the normalized pressure Δ𝑃𝑑 increases for a higher rotation

𝜔. The surging point at a higher rotation occurs at a lower inlet normalized mixture folwrate 𝑄𝑚𝑖𝑥 𝑖𝑛,𝑑𝑠𝑢𝑟𝑔𝑖𝑛𝑔

and corresponds

to a higher normalized developed pressure Δ𝑃𝑑𝑠𝑢𝑟𝑔𝑖𝑛𝑔

. This was also observed for different gas intake volumetric

fractions 𝜆𝑔,𝑖𝑛.

6.5 Surging Points

The surging points shown in Table 5 correspond to the maximum developed pressure samples ∆𝑃 obtained for each

performance test with constant 𝜆𝑔,𝑖𝑛 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

η [

% ]

-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 - λ_inlet=10 %

Single Phase ω=3600 rpm Single Phase ω=3000 rpm Single Phase ω=2600 rpm

ω=3600 rpm - λ_inlet=10 % ω=3000 rpm - λ_inlet=10 % ω=2600 rpm - λ_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

(ΔP/

ΔP

_sp

_max

) -

No

rmal

ize

d P

ress

ure


HGH Performance Test - P_in=300 kPa - λ_in=30 %

Single Phase

ω=3600 rpm

ω=3000 rpm

ω=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

λ_o

ut

[ %

] -

Ou

tlet

GV

F


HGH Performance Test - P_in=300 kPa - λ_in=30 %

ω=3600 rpm

ω=3000 rpm

ω=2600 rpm


Table 5 – Surging Points

Analyzing the data, none of the two-phase dimensionless numbers Π𝑖 was constant at the surging points. Figure 17

and Figure 18 show the normalized inlet mixture flow rate 𝑄𝑚𝑖𝑥 𝑖𝑛,𝑑𝑠𝑢𝑟𝑔𝑖𝑛𝑔

and the normalized developed pressure Δ𝑃𝑑𝑠𝑢𝑟𝑔𝑖𝑛𝑔

at the surging points represented as functions of the inlet gas volumetric fraction 𝜆𝑔,𝑖𝑛:

Figure 17 – Normalized inlet mixture flow rate at the surging points as a function of the inlet gas volumetric

fraction

ω [rpm] P_in [ kPa ] λ_in [% ] P1 [kPa] QL [m³/day] Qm_1 [m³/day] λ_1 [ % ] ΔP_12 [ kPa ] Qm1_d ΔP_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

λ_in [ % ] - Inlet GVF

HGH Performance Test - Surging Condition

(ω = 2600 rpm; P_in = 300 kPa)

(ω = 3000 rpm; P_in = 300 kPa)

(ω = 3600 rpm; P_in = 300 kPa)

(ω = 3600 rpm; λ_in = 30%; P_in = 100, 200, 300, and 400 kPa)


18

Figure 18 – Normalized developed pressure at the surging points as a function of the inlet gas volumetric fraction

The surging normalized mixture flow rate 𝑄𝑚𝑖𝑥 𝑖𝑛,𝑑𝑠𝑢𝑟𝑔𝑖𝑛𝑔

decreases and that the normalized developed pressure

Δ𝑃𝑑𝑠𝑢𝑟𝑔𝑖𝑛𝑔

increases as the rotation 𝜔 increases. There was a higher dispersion for 𝜆𝑔 𝑖𝑛 = 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 – Comparison between the single-phase and the surging points normalized curves

Comparison between Surging Point and Tests with 𝑸𝒈,𝒊𝒏 = 𝒄𝒕𝒆 for 𝝎 = 𝟑𝟔𝟎𝟎 𝒓𝒑𝒎 and 𝑷𝒊𝒏 = 𝟑𝟎𝟎 𝒌𝑷𝒂

The figure below shows that the points with maximum Δ𝑃 in the curves with 𝑄𝑔,𝑖𝑛 = 𝑐𝑡𝑒 do not correspond to the

surging points obtained in the 𝜆𝑔 𝑖𝑛 = 𝑐𝑡𝑒 tests for the same rotation (𝜔 = 3600 𝑟𝑝𝑚) and intake pressure (𝑃𝑖𝑛 =

300 𝑘𝑃𝑎):

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%

(ΔP/

ΔP

_sp

_max

) -

No

rmal

ize

d P

ress

ure

at

Surg

ing

λ_in [ % ] - Inlet GVF


(ω = 2600 rpm; P_in = 300 kPa)

(ω = 3000 rpm; P_in = 300 kPa)

(ω = 3600 rpm; P_in = 300 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

(ΔP/

ΔP

_sp

_max

) -

No

rmal

ize

d P

ress

ure

at

Surg

ing



Single Phase

(ω = 2600 rpm; P_in = 300 kPa)

(ω = 3000 rpm; P_in = 300 kPa)

(ω = 3600 rpm; P_in = 300 kPa)



Figure 20 – 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 Δ𝑃 are very close only for the 𝜆𝑔,𝑖𝑛 = 10% and 𝑄𝑔,𝑖𝑛 = 17 𝑚3 𝑑𝑎𝑦⁄ tests. For higher gas

volumetric flow rates 𝑄𝑔,𝑖𝑛 = 𝑐𝑡𝑒, the points of maximum Δ𝑃 are in a region between the single-phase curve and an

interpolated curve passing through the surging points (𝜆𝑔,𝑖𝑛 = 𝑐𝑡𝑒), 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 𝜆𝑔,𝑖𝑛𝑠𝑢𝑟𝑔𝑖𝑛𝑔

, could be expressed as the product of independent functions of the

following arguments: the rotation 𝜔; the normalized intake mixture flow rate 𝑄𝑚𝑖𝑥 𝑖𝑛,𝑑 ; and the gas to liquid specific

mass ratio at the intake, represented as 𝜌𝑔 𝑖𝑛

𝜌𝐿⁄ . Therefore:

��𝑔,𝑖𝑛𝑠𝑢𝑟𝑔𝑖𝑛𝑔

= 𝑓1(𝑄𝑚𝑖𝑥 𝑖𝑛,𝑑 ) 𝜔𝑏1 (𝜌𝑔 𝑖𝑛

𝜌𝐿

)

𝑏2

( 58 )

where:

𝑓1(𝑄𝑚𝑖𝑥 𝑖𝑛,𝑑 ) = ∑ 𝑎𝑚

3

𝑚=0

𝑄𝑚𝑖𝑥 𝑖𝑛,𝑑 𝑚

( 59 )

Assuming ��𝑔,𝑖𝑛𝑠𝑢𝑟𝑔𝑖𝑛𝑔

= 0 for 𝑄𝑚𝑖𝑥 𝑖𝑛,𝑑 𝑠𝑢𝑟𝑖𝑛𝑔

= 0, the general solution is 𝑎0 = 0. The fitting coefficients 𝑎𝑚 (for 𝑚 = 1 to

3), 𝑏1 and 𝑏2 were calculated by the Solver (Excel) minimizing the accumulated quadratic error 𝐸 defined as:

𝐸 = ∑(��𝑔,𝑖𝑛𝑠𝑢𝑟𝑔𝑖𝑛𝑔

− 𝜆𝑔,𝑖𝑛𝑠𝑢𝑟𝑔𝑖𝑛𝑔

)2

( 60 )

The following figure shows the original values 𝜆𝑔,𝑖𝑛𝑠𝑢𝑟𝑔𝑖𝑛𝑔

(horizontal-axis) and the correlation prediction ��𝑔,𝑖𝑛𝑠𝑢𝑟𝑔𝑖𝑛𝑔

(vertical-axis).

0

20

40

60

80

100

120

0 100 200 300 400 500 600 700 800

ΔP

[ k

Pa/

stag

e ]

-A

vera

ge P

ress

ure

Incr

em

en

t p

er

Stag

e


HGH Performance Test - ω = 3600 rpm - P_in = 300 kPa

Single Phase

Qg_in = 17 m³/day - Qg_in_d=0.0259

Qg_in = 34 m³/day - Qg_in_d=0.0518

Qg_in = 51.5 m³/day - Qg_in_d=0.0784

Qg_in = 68.6 m³/day - Qg_in_d=0.1045

Qg_in = 90 m³/day - Qg_in_d=0.137

Qg_in = 103 m³/day - Qg_in_d=0.1568

Qg_in = 128.6 m³/day - Qg_in_d=0.1958

Surging (ω = 3600 rpm; P_in = 300 kPa)


20

Figure 21 – Errors of the preliminary correlation for the inlet gas volumetric fraction at the surging point

There was a very poor fitting around 𝜆𝑔 𝑖𝑛 = 20%. It is therefore necessary to refine the test matrix around

𝜆𝑔 𝑖𝑛 = 20% and to adjust the coefficients of different base functions.

6.6 Two-Phase Efficiency

The figure below shows the HGH two-phase efficiency 𝜂 as a function of the inlet mixture volumetric flow rate

𝑄𝑚𝑖𝑥,𝑖𝑛 for 𝜔 = 3600 𝑟𝑝𝑚 and 𝑃𝑖𝑛 = 300 𝑘𝑃𝑎:

Figure 22 – 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 𝑄𝑚𝑖𝑥 𝑎𝑣𝑔 the two-phase efficiency 𝜂 decreases as the inlet gas volumetric

fraction 𝜆𝑔 𝑖𝑛 increases.

For a constant 𝜆𝑔 𝑖𝑛 there is a point of maximum two-phase efficiency. This point occurs at an intake mixture flow

rate 𝑄𝑚𝑖𝑥 ,𝑖𝑛𝐵𝐸𝑃 higher than the surging flow rate 𝑄𝑚𝑖𝑥 𝑎𝑣𝑔

𝑠𝑢𝑟𝑔𝑖𝑛𝑔.

0%

10%

20%

30%

40%

50%

60%

0% 10% 20% 30% 40% 50% 60%

Co

rre

lati

on

{ λ

_in

@ S

urg

ing

}

Objective { λ_in @ Surging }

Fitting Analysis: GVF at Intake Conditions for Surgingλ_sg = [ a1* (Qm_d) + a2*(Qm_d)^2 + a3*(Qm_d)^3] * (ω^b0) * (ρg_avg/ρL)^b1

ω = 2600 rpm; P_in = 300 kPaλ_in = 10, 20, 30, 40, and 50 %

ω = 3000 rpm; P_in = 300 kPaλ_in = 10, 20, 30, 40, and 50 %

ω = 3600 rpm; P_in = 300 kPaλ_in = 5, 10, 15, 20, 25, 40, and 45 %

ω = 3600 rpm; P_in = 100 kPaλ_in = 30%

ω = 3600 rpm; P_in = 200 kPaλ_in = 30%

ω = 3600 rpm; P_in = 300 kPaλ_in = 30%

ω = 3600 rpm; P_in = 300 kPaλ_in = 30%

Reference Line

Reference ± 10%

Reference ± 20 %

0%

10%

20%

30%

40%

50%

60%

0 100 200 300 400 500 600 700 800

η [

% ]

-Tw

o-P

has

e E

ffic

ien

cy

Qmix [m³/day] - Inlet Volumetric Flowrate

HGH Performance Test - ω=3600 rpm - P1=300 kPa

Single Phase

λ_inlet=5 %

λ_inlet=10 %

λ_inlet=15 %

λ_inlet=20 %

λ_inlet=25 %

λ_inlet=30 %

λ_inlet=40 %

λ_inlet=45 %

Surging[ Max ΔP for λ=cte ]

Two-PhaseIsothermal BEP


Additionally, as the 𝜆𝑔 𝑖𝑛 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 𝑃𝑖𝑛 , rotation 𝜔, intake mixture flow rate 𝑄𝑚𝑖𝑥,𝑖𝑛, and either the intake gas volumetric fraction 𝜆𝑔 𝑖𝑛 or

the intake gas volumetric flow rate 𝑄𝑔 𝑖𝑛.

The single-phase tests showed that the developed pressure Δ𝑃 and the liquid flow rate 𝑄𝐿 follow the affinity laws. It

was observed that the dimensionless BHP and the efficiency 𝜂 depended on the rotation 𝜔, 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

(𝑍 = 1) and considered an isothermal compression at an average temperature 𝑇𝑎𝑣𝑔 between the intake 𝑇𝑖𝑛 and the

outlet 𝑇𝑜𝑢𝑡 .

The two-phase tests showed that the equipment is able to pump mixtures with an intake gas volumetric fraction

𝜆𝑔 𝑖𝑛 up to 50 % with pressure gain and without surging. However, for high gas volumetric fractions 𝜆𝑔 𝑖𝑛, 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 𝜆𝑔 𝑖𝑛 . The

operational range between the open-flow and the surging reduce as the intake gas volumetric fraction increases.

In the performance tests with constant 𝜆𝑔 𝑖𝑛 , there was a reduction in the surging intake mixture flow rate 𝑄𝑚𝑖𝑥 𝑖𝑛𝑠𝑢𝑟𝑔𝑖𝑛𝑔

and an increase in the developed pressure Δ𝑃𝑠𝑢𝑟𝑔𝑖𝑛𝑔 for a higher intake pressure 𝑃𝑖𝑛 .

Normalized variables were used in order to compare the HGH performance at different rotations 𝜔. For a constant

intake pressure 𝑃𝑖𝑛 and volumetric gas fraction 𝜆𝑔,𝑖𝑛 the normalized surging flow rate 𝑄𝑚𝑖𝑥 𝑖𝑛𝑠𝑢𝑟𝑔𝑖𝑛𝑔

decreased and the

normalized developed pressure Δ𝑃𝑑,𝑠𝑢𝑟𝑔𝑖𝑛𝑔 increased for a higher rotation 𝜔. Due to the higher pressure gain Δ𝑃 there

was also a reduction in the outlet gas volumetric fraction 𝜆𝑔,𝑜𝑢𝑡.

None of the two-phase dimensionless numbers Π𝑖 was constant at the surging points. More effort is required to

develop a surging correlation.

For a constant rotation 𝜔, intake pressure 𝑃𝑖𝑛 , and gas volumetric pressure 𝜆𝑔,𝑖𝑛 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 Mecânica, 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)

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10. RESPONSIBILITY NOTICE

The author is the only responsible for the printed material included in this paper.

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