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Multiphase Flows

# An Algorithm for Determining Volume Fractions in Two-Phase Liquid Flows by Measuring Sound Speed

[+] Author and Article Information
Anirban Chaudhuri1

Sensors and Electrochemical Devices (MPA-11), Los Alamos National Laboratory, Los Alamos, NM 87545anirban@lanl.gov

Curtis F. Osterhoudt2

Sensors and Electrochemical Devices (MPA-11), Los Alamos National Laboratory, Los Alamos, NM 87545cfo@lanl.gov

Dipen N. Sinha

Sensors and Electrochemical Devices (MPA-11), Los Alamos National Laboratory, Los Alamos, NM 87545sinha@lanl.gov

From the definition of oil-cut, $φ=Vo/(Vo+Vw)$, where it is assumed that the two components, oil and water in this case, are immiscible, and the total mixed volume is the sum of the individual volumes $Vo$ and $Vw$. Applying conservation of mass, $ρ(Vo+Vw)=ρoVo+ρwVw⇒ρ=ρoφ+ρw(1-φ)$.

1

Corresponding author.

2

J. Fluids Eng 134(10), 101301 (Sep 28, 2012) (7 pages) doi:10.1115/1.4007265 History: Received October 04, 2011; Revised July 19, 2012; Published September 24, 2012; Online September 28, 2012

## Abstract

This paper presents a method of determining the volume fractions of two liquid components in a two-phase flow by measuring the speed of sound through the composite fluid and the instantaneous temperature. Two separate algorithms are developed, based on earlier modeling work by Urick (Urick, 1947, “A Sound Velocity Method for Determining the Compressibility of Finely Divided Substances,” J. Appl. Phys., 18 (11), pp. 983–987) and Kuster and Toksöz (Kuster and Toksöz, 1974, “Velocity and Attenuation of Seismic Waves in Two-Phase Media: Part 1. Theoretical Formulations,” Geophysics, 39 (5), pp. 587–606). The main difference between these two models is the representation of the composite density as a function of the individual densities; the former uses a linear rule-of-mixtures approach, while the latter uses a nonlinear fractional formulation. Both approaches lead to a quadratic equation, the root of which yields the volume fraction ($φ$) of one component, subject to the condition $0≤φ≤1$. We present results of a study with mixtures of crude oil and process water, and a comparison of our results with a Coriolis meter. The liquid densities and sound speeds are calibrated at various temperatures for each fluid component, and the coefficients are used in the final algorithm. Numerical studies of sensitivity of the calculated volume fraction to temperature changes are also presented.

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## Figures

Figure 1

Measured sound speeds and densities of the constituent crude oil and processed water components with varying temperature in two different sets of samples (from oil fields 1 and 2)

Figure 2

Change in nondimensional parameters r=ρo/ρw, κo/κw, and φ as a function of temperature. Solid lines are for samples from oil field 1, while samples from field 2 are represented by dashed lines. The values of φ were calculated for two different sound speeds, 1450 m/s and 1500 m/s. The values of r change from 0.883 to 0.867 for oil field 1, and from 0.787 to 0.773 for oil field 2.

Figure 3

Variation in calculated oil-cut as a function of measured sound speed (using Kuster–Toksöz model), at different temperature levels that are characteristic of the respective field

Figure 4

Variation in calculated oil-cut as a function of measured temperature (using Kuster–Toksöz model), at different sound speeds

Figure 5

Calculated values of φ for a range of values of c. r=0.8 was selected for this plot.

Figure 6

Comparison between different methods of oil-water fraction determination at two oil fields, where “new model” refers to the algorithm developed in this paper starting from the Kuster–Toksöz model. Note that the y-axes are in terms of percentage water-cut.

Figure 7

Sensitivity of oil-cut calculation on changes in independent measurements for samples from oil field 1

Figure 8

Sensitivity of oil-cut calculation to changes in independent measurements for samples from oil field 2

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