*2.3. Liquid Flow Rate Measurement Accuracy*

It is rather straightforward to compute the average liquid flow rate once the instantaneous liquid holdup and liquid flow velocity correlation is available. Assuming a statistically representative sample of the correlation is obtained by taking a total of *N* measurements, the average liquid flow rate may be computed as the average of the point-by-point product of liquid holdup and velocity, multiplied by the area of the pipe, i.e.,

$$
\langle \mathbf{Q}\_{\rm liq} \rangle = \frac{A\_{\rm pipe}}{N} \sum\_{i=1}^{N} h\_{\rm liq,i} u\_{\rm liq,i} \,. \tag{5}
$$

Figure 7 shows the relative liquid flow rate error as a function of the reference liquid flow rate for all experiments presented in Figure 4 together with an ±5% error band that is the generally accepted liquid flow rate accuracy required in multiphase flow metering (dashed lines) [12] and the relative error that corresponds to a zero-point inaccuracy of ±1 m3/h (dotted lines) that is commonly accepted as a practical limit for the accuracy of multiphase flow metering systems at low liquid flow rates [2]. The relative flow error is within the ±5% error band for all but four flow experiments. No difference in flow accuracy is observed between the flow experiments that had free flow or were disturbed by the downstream valve.

**Figure 7.** The relative liquid flow rate error as a function of reference liquid flow rate for all multiphase flow experiments that were presented in Figure 4. The dashed lines represent a ±5% error band that is the generally accepted liquid flow rate accuracy required in multiphase flow metering. The dotted lines represent the relative error that corresponds to a zero-point inaccuracy of <sup>±</sup>1 m3/h that is commonly accepted as a practical limit for the accuracy of multiphase flow metering systems at low liquid flow rates.
