multiphase flow through centrifugal pumps

MULTIPHASE FLOW THROUGH CENTRIFUGAL PUMPS

Dr. Rajesh Sachdeva, Dr. D. R. Doty and

Dr. Z. Schmidt

MULTIPHASE FLOW THROUGH CENTRIFUGAL PUMPS

bY

DR. RAJESH SACHDEVA, University of Tulsa (presently with Simulation Sciences Inc.) DR. D.R. DOTY AND DR. 2. SCHMIDT (both of University of Tulsa)

ABSTRACT

Recently, there has been considerable interest in the petroleum industry on multiphase flow through pumps. Pumping gassy fluids has applications in both pipeline and electric submersible pumps. The present study discusses a dynamic and a correlational model for three electric submersible pumps (ESP’s).The dynamic model is applicable to pipeline centrifugal pumps (since the flow physics is exactly the same) provided a correlation for bubble size is known.

INTRODUCTION

Centrifugal forces dominate gravitational forces in multiphase impeller flow. As such, it has been shown by investigators that the diffuser performance can be ignored and impeller behavior determines centrifugal pump behavior. The basic model presented in this paper is develoiped for electric submersible pumps (ESPs) but is equally applicable for gas-liquid flow through any centrifugal (radial or axial-type) pumps. This paper heavily draws on parts of papers presented elsewhere by the same authors’*3*4*5 . The interest in developing an offshore multiphase pump has been mainly due to major economic benefits associated with laying a single multiphase pipeline (as opposed to one gas and one liquid pipeline). Development and modelling multiphase pipeline pumps is becoming more important as the oil companies are venturing further into the sea for oil. Data from an Amoco-Centrilift study’ were

used to validate the model developed. There have been quite a few studies in the nuclear industry3 on modelling impellers. It has been shown’ that none of the models of the nuclear industry can be used for ESPs in gassy wells, This is because the nuclear industry models are pump specific, applicable to substantially lower void fractions, and do not consider the effects of inlet pressure. The development of a general model for multiphase flow through centrifugal pumps would be a complicated task primarily because of complex pump geometries. A two-dimensional multiphase pump model would require the knowledge of phasic holdup and velocity profiles in a pump and this data is not at all easy to measure. The results show very encouraging performance prediction for both the radial and axial pumps. Limited success was also obtained in correlating the pump pressure increase (Model 2). Performance of axial and radial pumps is also compared.

PREVIOUS WORK

Most of the work on multiphase flow through ESPs has been done in the nuclear industry. A comprehensive review is given by Sachdeva3. The nuclear industry models cannot be used because of reasons cited earlier and will not be discussed.

2 MULTIPHASE FLOW THROUGH CENTRIFUGAL PUMPS

The work in the nuclear industry can be summarised into three main phases:

4

b)

c)

Black Box Methods: These were largely unseuccessful. Investigators realised thatat least a qualitative idea of the flow physics inside the pump was required.

Experimented Studies: Various U.S. and Japanese investigators3 qualitatively studied the movement of the gaseous phase within the impeller. It was found that bubbly flow caused lower head degradation than slug/churn-turbulentflow. Investigators also found that the gas slug growth around the impeller eye led to unstable flow towards the left-hand side of the pump (rate-head) curve.

Analytical Models: basic one-dimensional, multiphase pump models were developed by investigators. The most motable works wete these of Zakem6 and Furnya’ The basic model was the same in both cases but the solution methods were slightly different. Both ignored effects of pump inlet pressure and gas compressibility. Neither had good success in correlating with experimental data.

Studies in the petroleum industry include:

(a) Lea and Bearden’: This study consisted primarily of gathering data for the K-70, I-42B and C-72 pumps and a demonstration that under certain conditions, gas through an ESP may be advantageous because of a gas lift effect. The present study uses the data gathered by Lea and Bearden.

(4 Tarpley4: Here, the author presented an extremely simplistic model for pump head degradation in an ESP. The energy required to compress the gas was taken to be the only factor contributing to head degradation. As the results of the study show, this energy has a negligible effect on the pump head degradation. The method did not appear to work for inlet gas void fractions over 2%. Note that below 2%, there is hardly any pump head degradation and thus this model is of extremely limited use.

Limited amount of Russian literature3 is also available on the subject. Although, the Russians were among the first

to study the problem, their literature seems to be the least advanced. None of their models involved the study

of the actual flow physics in a pump.

MODEL FORMULATION

Modelling single phase flow through ESP, can easily give 50% errors, when approached within a one-dimensional framework3. For comparison, errors for single-phase flow in tubulars are around l-2%. The pump geometry and a rotating impeller are the primary complicating factors for modelling two-phase flow through ESPs. Furthermore, in multiphase flow, the effects of impeller slip (different from interphasic slip to be discussed later) are unknown. In single phase flow, the impeller slip causes the velocity triangle to deviate from the ideal velocity triangle as shown in Figure (1). The net effect of this deviation is a reduction in useful head produced’. Also, individual pump losses (mechanical, hydraulic, etc.) have not yet been adequately quantified even for single-phase flow. Given the minimal amount of knowledge for single-phase flow through ESPs, formulation of a simplified multiphase model becomes necessary. This avoids assumptions that cannot be corroborated.

Sachdeva’, through numerous runs, has shown that diffuser performance can be neglected. Similar conclusions were also reached by Pate1 and Runstadler’, Runstadler and DoIan” and Hench and Johnston”. Since the data” shows that the impeller dominates the pump performance, the diffuser performance is ignored.

The basic procedure for a pump model is as under:

(a) develop a simple, one-dimensional liquid-only model. Since most losses are not considered, this model will not match the actual curves

(b) formulate a similar one-dimensional, multiphase model

(c) the difference between (a) and (b) will represent the additional head degradation due to free gas in the

’ pump. This difference is subtracted from the liquid- only curve published by the manufacturer. This approach is represented in Figure (2).

IDEALISED MULTIPHASE CURVE

This section deals with the development of the curve (B) shown in Figure (2). Noemenclature used is shown in Figure (3). The l-42, K-70 and C-72 pumps are shown in Figure (4).

Flow is assumed to be idealised, i.e., no recirculation, no impeller slip (different from interphasic slip), etc. Diffuser

3

performance is ignored for reasons discussed earlier. A two-fluid approach is used for multiphase equations.

Continuitv Equations

Along a streamline z, “parallel” to the impeller blades, the phasic continuity equations for gas and liquid are given by:

M, = P&4

ML = pr W, (1 -a) A,

Differentiation yields:

I dA, 1 da --+-- I dWg 1 dps 0 A, dz a dz +Tqdz+p,dz=

I dA, 1 da -- ’ dW’=() ---+-- A, dz (1 -a) dz W, dz

. ..(I)

. ..(2)

. ..(3)

. ..(4)

These equations are valid for both bubbly and churn- turbulent flow regimes.

Momentum Equations

One-dimensional phasic momentum equations for steady state flow are given by Wallis’* as:

Yl PLVrf ar =q+WL-; +$mL . ..(5)

av, PA ar . ..(6)

Here, Zb, and Zb, are the body forces and Zf, and Zf, are “leftover” or “balancing” forces.

In an axial pump, the following geometrical relationship is true:

d’ = sir-$?(f) cosy(f) dz

. ..(7)

Based on Equation (7) the following can also be shown to be true for an axial pump:

h = W,sin#?(f) cosy(f) . ..(8)

and,

4 = A@-$(/) cos&) . ..(9)

Thus, the relationship between various velocity components can be easily determined at any point along the impeller path. Note that the angle y=O” for a flat radial pump.

The body forces due to the impeller can be represented as:

rbg = p, Q2f . ..(lO)

and

xb, = pL Q2f . ..(I 1)

The expressions for body forces are not dependent on the flow regime in the impeller. The rest of the section deals with the computation of the “balancing” forces.

If bubbly flow is assumed to exist in the impeller, the drag forces that increase the gas-liquid velocity lag can be represented as3”*:

f drag& = - CD a (1 -a)2.78

and

f draga =c, ’ (1 -a)‘.” P‘IYL . ..(13)

The drag forces reduce useful head produced and the above expressions account for the effects of bubble swarm (particle-particle forces). For churn-turbulentflow, the term C-,/r,, in Equations (12) and (13) is usually’2*‘3 replaced by a function of (l-a). This reflects reduced value of C-Jr,, implying vastly increased gas-liquid velocity lag. Thus, in churn-turbulentflow, the liquid


phase accelerates more causing the useful pump energy to be wasted as liquid velocity head.

The apparent mass forces exist for bubbly flow and tend to reduce the gas-liquid velocity lag. In churn-turbulent flow, these forces do not exist by definition. However, we have retained these forces in the model since the transition point between bubbly and churn-turbulentflow is not known in the impeller. The retention of these forces in the churn-turbulentflow regime causes a slight error. This error is absorbed by the Cdr,, correlation. The advantage of doing this is that the bubble to churn- turbulent flow pattern transition boundary within the impeller need not be known.

The liquid and gas apparent mass terms are given as:

f amg = -C/3& -$ Kl - V,)

and.

f amc = C(y- ,aa)P‘Yg 2 (Kg - V,)

In absence of any information, a spherical bubble shape (C=OS) is assumed.

The frictional forces for each phase are calculated as suggested by Craveri and Wallis” and given in Sachdeva3.

Equations (5) (1 l), (12) and (15) collectively represent the momentum equation for the liquid phase. The gas phase is represented by Equations (6), (IO), (13) and (14). The approximate frictional term is added as explained in Reference (1). The necessary geometrical relationships for the axial impeller is given by Equations (7) and (9).

For liquid-only flow, either Equation (5) or (6) can be shown to reduce to:

g dP = Q2r -- PL df

- + $3 . ..(16)

The relationship between r and z requires knowledge of the geometry of the pump. Since about 100 steps are required to integrate along the impeller streamline, a linear relationship between inlet and outlet /?-angle is assumed.

Note that /I is the angle between the velocity components U and V. Thus,

where

. ..(17)

. ..(18)

The y-angle is constant for the axial K-70 pump. With the above assumptions Equation (7) can be expressed as:

. ..(19)

Integration of Equation (19) yields the following relationship between r and z valid for an any pump:

z=F logtan [

W-f,) +B, -logtan w, -fJ +B, 2 2 1 420)

Note, y=O for a radial pump.

Equation of State

The liquid is assumed to be incompressible. The gas phase is assumed to behave adiabatically:

p I - =c

Y

Pg

.I ..(21)

Integration of the above curve will yield the curve (A) in Figure (2).

5

Differentiation yields:

dP y-l G?J

-& - c 'Y&a -& = 0 . ..(22)

Note that the curve (B) in Figure (2) can be obtained from the equations of continuity, momentum and state once the appropriate value of Cdr,, is known.

MODEL SOLUTION

The solution vector [dw,/dz, dw$dz, dp$dz, da/dz, dP/dz] and is solved along each point of the impeller and for each flow rate. Since C&, is unknown, trial-and- error runs yielded C,Jrb value for each data point. This was then correlated in the following form:

CD pi,” -= K- rb a: OF

. ..(23)

Based on 326 diesel-CO, data points2*3, the following values were obtained for the axial K-70 pump:

K = 9.53 x lO-4 El = 3.33 E2 = 2.83 E3 = 5.92

For comparison, the radial C-72 pump of similar size as the axial K-70 pump gives (173 points):

K = 6.65 x 10” El = 5.21 E2 = 5.22 E3 = 8.94

Similarly, for the l-42 pump (287 points):

K = 5.7 x 10” El = 2.36 E2 = 6.64 E3 = 5.87

The regression analysis coefficients for the correlations for l-42, K-70 and C-72 pumps were respectively 92%, 94% and 90%. Diesel-CO, data were used for all cases. In absence of stage-to-stage pressure rise data, a linearly-averaged stage was correlated for.

RESULTS OF THE DYNAMIC MODEL

Some of the model trends are given in Figures (5) thru (16). Figures (5) through (8) show the model performance for the axial K-70 pump and Figures (9) through (12) for the radial C-72 pump (of similar size as the K-70 pump), and Figures (13) thru (16) for the l-42

pump. The error analysis for the dynamic model is shown in Table (1). For comparison purposes the pressure rise per stage (at bep) for each pump is also included. The dynamic model predicts the head degradation well.

The predictions for phasic velocities, void fractions, etc. are consistant with the observations of the photographic studies discussed in the earlier study’. Both pressures and gas densities increase along the impeller path as does the void fraction, This causes the ratio w,.& to decrease drastically towards the impeller exit as shown in Figure (17). The model thus shows acceleration of the liquid phase and the loss of useful head as liquid velocity head. For the radial or the axial pumps, for r,=O.l mm or so, there is hardly any head degradation predicted. Also, at large void fractions and lower inlet pressures, the gas phase velocity is drastically reduced and the gas phase almost “stalls” causing surging and eventually gas locking. All of the above predictions agree with the photographic evidence.

The gas-liquid slip is essential to quantifying multiphase head degradation. Under assumotions of no aas-liauid slip, the model will not predict anv head dearadation.

CORRELATIONAL MODEL (Model 21

The main disadvantage of the dynamic model is that it is complicated to solve for. To overcome this, approximate correlations were developed correlating the pressure increase per stage, pump inlet pressure, pump inlet void fraction and the liquid flow rate. Various parameters were tried and the best results were obtained from the following:

AP = K (P$’ (ain)= (QJ’”

Here AP is in psi per stage, P, is the pump stack inlet pressure in psig, a, is the pump stack inlet void fraction (not percent) and Q, is in gallons/min. For the radial I- 42B pump (287 points):

K = 1.154562, El = 0.943308, E2 = -1.175596 and E3 = -1.300093

For the radial C-72 pump (173 points):

K= 0.1531026, El = 0.875192,E2 = -1.764939, E3 = -0.918702

Finally, for the axial K-70 pump (326 points):

K = 0.0936583, El = 0.622180, E2 = -1.350338, E3 = -0.317039


The regression analysis coefficients for the l-42, C-72 and K-70 pumps were 70.63%, 87.66% and 85.12% respectively. All data are diesel-CO, data.

In predicting the pressure increase in ESPs, this correlation performed substantially worse than the dynamic model.

Table (1) compares errors from the dynamic and the correlational models. Excepting for the C-72 pump, errors from the correlational model (Model 2) are about 2 to 3 times those obtained from the dynamic model. However, the correlational model is extremely easy to use and an engineer can use this model for approximate estimates.

PUMP DESIGN (AXIAL verses RADIAL) AND ORIENTATION

The axial K-70 and the radial C-72 pumps are similar in dimensions and their performance will be compared here. In general, the axial pump suffers less degradation than the radial pump. This trend can be seen in Figures (5) through (12). The reader can compare Figures (5) and (9) Figures (6) and (10) and so on until Figures (8) and (12) and see that in general, the axial pump performs better. The dynamic model predicts this trend.

Another useful parameter to compare is the C,,/rb value for the K-70 and C-72 pumps. For the same values of a, P, and Q,, the value of Cdr,, is lower for the radial C-72 pump compared to that for the K-70 pump. This implies that the gas-liquid velocity lag will be lower in the axial K- 70 pump. Thus, the liquid phase will be accelerated less in the K-70 pump and less head will be lost as velocity head. This explains why the radial pump of comparable size performs worse than an axial pump. The higher C,Jrb value is also reflective of a pump’s tendency to have bubbly rather than churn-turbulent flow. Pump manufacturers should strive for hiaher G/Jr, values. This can be done by avoiding or breaking up the churn- turbulent regime. Reference (14) is an example of a patent application for a two-phase pump that tries to break up the bubbles and “mix” a churn-turbulentflow regime into a bubbly regime.

Note that the ratio of centrifugal to gravitational forces is about 150 or more even in ESP’s with diameters of 2-4 inches. This ratio will obviously be even higher for pipeline pumps. This suggests that (i) the pump orientation (vertical versus horizontal) does not effect the model, (ii) The model can be used to model the performance of multiphase pipeline pumps currently under development. Indications are that C,,/r,,will be the

only correlating parameter required.

CONCLUSIONS

1)

2)

3)

4)

5)

Dynamic model is developed and successfully tested against data from three centrifugal pumps of both radial and axial geometries.

Flow physics in impellers is extremely complex and simplistic, correlational approach (eg. Model 2) will have only limited success.

C,,/rb seems to be the only parameter required to complete the dynamic model for gas-liquid flow through any centrifugal pump.

The model agrees with the photographic studies in terms of: a) void fraction distribution in an impeller b) gas-liquid velocity ratio behavior c) explaining pump instability at lower liquid rates

(left of the best-efficiency point, bep)

The model gives the manufacturers a tool to design multiphase centrifugal pumps. Conventional single- phase flow dynamics is obviously totally inapplicable to model multiphase centrifugal pumps.

NOEMENCLATURE

Symbol Description

A b c

CLY El,E2,E3 f

i M

; Q r u V W

Area, @ body forces apparent mass coefficient, dimensionless drag coefficient, dimensionless exponents leftover forces gravitational constant constant mass rate (Ibm/s) exponent pressure (psi) flow rate radial coordinate peripheral velocity (Ws) absolute fluid velocity (ft/s) fluid velocity relative to the impeller (Ws)

GREEK

Symbol Description

e

; a Y

density, Ibm/ft! angular impeller velocity, radians/s blade angle, degrees void fraction (fraction) blade angle (r-z plane), = 0” for radial pumps adiabatic exponent

SUBSCRIPTS

Symbol Description

1 2 am drag

Y r Z

inlet outlet apparent mass drag gas liquid radial coordinate streamline coordinate (parallel to blades)

ACKNOWLEDGEMENTS

The author wishes to thank the Society of Petroleum Engineers for allowing copyright release of the material of this paper previously presented in SPE papers SPE22767 and SPE24328. Thanks are due to Ms. Vira Estrada for preparing the manuscript.

REFERENCES

1.

2.

3.

Sachdeva, R., Doty, D. R. and Schmidt, Z.: “Performance of Electric Submersible Pumps in Gassy Wells“, SPE 22767, presented at the 66th Annual Technical Conference and Exhibition of SPE, Dallas, TX, Oct. 6-9, 1991, accepted for publication.

Lea, J. F. and Bearden, J. L.: “Effect of Gaseous Fluids on Submersible Pump Performance”, JPT, December 1982 and SPE 9218.

Sachdeva, R.: Two-Phase Flow Throuqh Electric Submersible Pumps, Ph.D. dissertation, University of Tulsa, Tulsa, OK, 1988.

4.

5.

6.

7.

8.

9.

10.

11

12.

13.

14.

Sachdeva, R. et. al.: “Performance of Axial Electric Submersible Pumps in a Gassy Well”, SPE24238, presented at Casper, WY, May 18-21, 1992.

Sachdeva, R.: “Understanding Multiphase Dynamics in ESP’s for Better Multiphase Pump Design” presented at the Electric Submersible Pump workshop in Dallas, TX, 1992.

Zakem, S.: “Determination of Gas Accumulation and Two-Phase Slip Velocity in a Rotating Impeller”, Journal of Fluids Engineering, Vol. 102, 446-455, (December, 1980).

Furuya, 0.: ‘An analytical Model for Prediction of Two-Phase (non-condensable) Flow Pump Performance”, Journal of Fluids Engineering, Vol. 107, 139-147, (March, 1985).

Stepanoff, A. J.: Centrifuaal and Axial Flow Pumps, published by John Wiley and Sons, (1957).

Patel, B. R. and Runstadler, P. W.: “Investigations Into the Two-Phase Behavior of Centrifugal Pumps,” ASME Symposium on Polyphase Flow in Turbomachinery, (December lo-15 1978) San Fransisco.

Runstadler, P. W. and Dolan, F. X.: ‘Two-Phase Flow Pump Data for a Scale Model NSSS Pump,” ASME Symposium on Polyphase Flow in Turbomachinery, 65-73, (December 10-15, 1978) San Fransisco.

Hench, J. E. and Johnston, J. P.:‘Two-Dimensional Diffuser Performance with Subsonic, Two-Phase, Air- Water Flow,” Journal of Basic Engineering, (March, 1972), 105120.

Wallis, G. B.: One-Dimensional Two-Phase Flow, McGraw Hill Book Co., (1969).

Craver, M. B.: “Numerical Computatuon of Phase Separation in Two-Phase Flow,” Journal of Fluids Engineering, 147-153, Vol. 106, (June, 1984).

U K Patent Application, 982193533A, Application Number 8718564, (February, 1988). Application filed by Nuovopignone-lndustrie Meccaniche E Fonderia, S.p.A., Italy.


SI METRIC CONVERSION FACTORS

bbl x 1.589 873 E-01 = m3 ft x 3.048 E-01 =m in x 2.540 E-02 = m Ibm x 4.535 924 E-01 = kg psi x 6.894 757 E+OO = kPa

TABLE 1

Error Comparisons for Dynamic and Correlational Models

DYNAMIC CORRELATIONAL MODEL MODEL

(MODEL 2)

ABSOLUTE PRESSURE AVERAGE AVG. ERROR STANDARD ABSOLUTE STANDARD RISE AT BEP

ERROR PUMP

(PSI) DEVIATION AVG. ERROR DEVIATION FOR 100% (PSI) (PSI) (PSI) (PSI) DIESEL

l-42 -0.29 1.09 1.35 3.19 4.64 14.20

C-72 -0.34 1.61 1.66 1.49 2.02 11.43

K-70 1.06 1.27 2.07 5.03 5.52 15.93

I ACTUAL I

vu2

Figure I: Effect of slip on outlet velocity triange

A THEORETICAL PRESSURE

B RISE (LIQUID)

-- -m-- ‘THEORETICAL PRESSURE RISE (29PHASE)

PUBLISHED PRESSURE RISE (LIQUID) PREDICTED PRESSURE

-PHASE)

FLOW RATE

Figure 2: Dynamic model formulation

I I

I = IMPELLAR 1NLE.T 2= IMPELLAR OUTLET

Figure 3: Noemencalture

L42B

C-72

K-70

Figure 4: Pump geometries

- -

0 0 1000 2000 i‘ 3000 4000 5000

FLOW RATE (bbl/d)

- 100% LIQUID - 100% LIQUID 2=PHASE, ACTUAL 2=PHASE, ACTUAL

0 2=PHASE, PREDICTED 0 2=PHASE, PREDICTED

Figure 5: Dynamic Model Predictions (K-70): Pin = 60 psig, 9.92% gas

20

. 0

I U L-PHr -

-

0 A

A ‘““7o L’QU’D 7 :I ‘ASE, ACTUAL 0 2=PHASE, PREDICTED

-

1

I,_ I, n u 1000 2000

FLOW RATE (bbl/d) 4000 5000


2000 3000 FLOW RATE (bbl/d)

4000 5000


25

20

F s W 15 ctl 3

%I0 W Qi n

5

0

- 100% LIQUID n 2-PHASE, ACTUAL 0 Z-PHASE, PREDICTED

0 2000 3000 4000 5000 FLOW RATE (bbl/d)

Figure 9: Dynamic Model Prediction (C-72): Pin = 55 psig, 9.92% gas

25

20

e 5 e_ 15 w OL 3 z -lo W 111: e 5

0

- 100% LIQUID n 2=PHASE, ACTUAL 0 Z-PHASE, PREDlCTED

8

-

-

I I * I I

0 1000 2000 3000

FLOW RATE (bbl/d)

4000 5000


25

- n

100% LIQUID 2=PHASE, ACTUAL

20 --

f 0 2=PHASE, PREDICTED

0 1000 2000 3000

FLOW RATE (bblld)

1000 5000


25

20

0 2000 3000

FLOW RATE (bblld)

- 100% LIQUID n 2=PHASE, ACTUAL 0 2=PHASE, PREDICTED


Figure 13:

- 100% LIQUID ZPHASE, ACTUAL

0 2-PHASE, PREDICTElI

0 500 1000 1500 2000 2500 3000

FLOW RATE (bbl/d)

Model Predictions: I-42B pump, Pin=60 psig, in=5.67%, Diesel-CO2

- 100% LIQUID n 2=PHASE, ACTUAL 0 2-PHASE, PREDICTED

FLOW RATE (bblld)

Figure 14: Model Predictions: I-42B pump, Pin=95 psig, in=30%, Diesel-CO2

loo0 1500 2000

FLOW RATE (bblld) 2500

Figure 15: Model Predictions: L42B pump, Pin=280 psig, in=30%, Diesel-C@

20

15

10

5

0

Figure 16:

- 100% LIQUID 2-PHASE, ACTUAL 2=PHASE, PREDICTED

-

0 500 loo0 1500 2000 2500 3000

FLOW RATE (bbl/d)

Model Predicitons: I-42B pump, Pin=280 psig, in=39.94%, Diesel-CO

a STAGE 1 d

I I = IMPELLER D = DIFFUSER

4 STAGE 2 4r STAGE 3 --~

a- b---++---D-w-----L---w+- D---c~~---I -c-)+----D -w

Figure 17: Multistage pump behavior

multiphase flow through centrifugal pumps

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