# Pressure Drop Measurements in Venturi Meters of Different Beta Ratios for Oil–Water Flow Experiments

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## Abstract

The performances of the venturi meters for oil–water flow under real oil well operating conditions were investigated in the present experimental investigation. The pressure drop measurements were studied in Tercom flanged machined venturi meters with a beta ratio (\(\beta )=0.4\), 0.5 and 0.6 for oil–water two-phase flow experiments in a 0.0762 m (3-in.) pipe. The experimental data for different fluid mixture flow rates and water cuts were acquired using a two-phase, large-scale inclinable flow loop. Potable water and Exxsol mineral oil (D80) were used for the single-phase and two-phase oil–water experiments for the three venturi meters. The experiments were conducted for water cuts varying from 0 to 100% in steps of 20%, flow rates ranging from 2000 to 10,000 barrels per day (bpd), and for horizontal and vertical flow loop inclinations (\(0{^{\circ }}\) and \(90{^{\circ }}\)). Real oil wells flow rates were matched by selecting test liquid flow rates. The experimental results showed that the venturi pressure drop varies as the square of the fluid flow rate for given water cut through the venturi meters studied. For given flow rate and water cut, the venturi pressure drop is inversely proportional to the venturi \(\beta \); however, the venturi pressure drop varies almost linearly with the water cut for a given fluid flow rate. Within the range of test fluid flow rates, the venturi pressure drop measurements were unaffected by the inclination of the three venturi meters studied in the flow loop. This is very important from an application standpoint.

## Keywords

Oil–water Venturi meters Beta ratio Inclination Pressure drop Multiphase flow meter## List of symbols

*k*Modified venturi discharge coefficient (\(\hbox {m}^{2}\) s/h)

- \(\beta \)
Venturi beta ratio

- \({A}_{\mathrm{t}}\)
Throat cross-sectional area (\(\hbox {m}^{2}\))

- \({A}_{\mathrm{p}}\)
Pipe cross-sectional area (\({\mathrm{m}^{2}}\))

*D*or \({D}_{\mathrm{h}}\)Hydraulic diameter (m)

- \({C}_{\mathrm{d}}\)
Venturi discharge coefficient

- \(\hbox {Cp}_{\mathrm{m}}\)
Mixture venturi pressure coefficient

- \(\lambda \)
Water volume fraction or water cut

- \({Q}_{\mathrm{m}}\)
Mixture flow rate (\(\hbox {m}^{3}/\hbox {h}\))

- \({Q}_{\mathrm{meas}}\)
Measured fluid mixture flow rate (\(\hbox {m}^{3}/\hbox {h}\))

- \({Q}_{\mathrm{cal}}\)
Calculated fluid mixture flow rate (\(\hbox {m}^{3}\)/h)

- \(\theta \)
Inclination angle (degrees)

- \(V_{\mathrm{m}}\)
Mixture average velocity at venturi inlet (m/s)

- \({Re}_{\mathrm{m}}\)
Mixture Reynolds number

## Greek symbols

- \(\Delta {P}\)
Venturi pressure drop (Pa)

- \(\upsilon _\mathrm{m}\)
Mixture kinematic viscosity (m\(^{2}\)/s)

- \(\mu _\mathrm{m} \)
Mixture dynamic viscosity (Pa s)

- \(\mu _\mathrm{w} \)
Water dynamic viscosity (Pa s)

- \(\mu _\mathrm{o} \)
Oil dynamic viscosity (Pa s)

- \(\rho _{\mathrm{m}}\)
Fluid (or liquid) mixture density (\(\hbox {kg/m}^{3}\))

## Subscripts

*o*Oil

*w*Water

*m*Mixture

*t*Venturi throat

*p*Pipe

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## Notes

### Acknowledgements

The authors gratefully wish to acknowledge the support provided by Saudi Aramco, Dhahran, Saudi Arabia, for funding this work through Project No. CER02386. Also the Center of Engineering Research (CER) at the Research Institute of King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, is acknowledged, for their technical support to complete this research work.

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