Piecewise Gilbert-type correlation for two-phase flowback through wellhead chokes in hydraulically fractured shale gas wells

Wellhead chokes play key roles in liquid-flowback and gas-production processes of hydraulically fractured shale-gas wells. The characteristic of choke flow is quite complex and involves many factors, such as choke size, pressure and liquid-gas ratio (LGR). Gilbert-type correlations have been widely used in choke flow studying, but they are empirical and their accuracy is easily affected by operational conditions or special reservoir properties. Therefore, it is worth paying attention to the applicability of Gilbert-type correlation. This paper collected over 10,000 sets of data from 12 shale gas wells in Changning region, analyzed the influence of LGR on the prediction accuracy of Gilbert-type correlations, and developed a new correlation named Piecewise Gilbert-type Correlation (PGC) for gas-liquid two-phase flow through chokes. The results showed that LGR had a great impact on the prediction accuracy, and therefore the LGR data during the flowback period could be divided into several stages for data-fitting separately. PGC was established on multiple LGR stages, which led to multiple different groups of empirical coefficients, and had been proved to be more accurate on the whole. Specifically, the overall error and the mean error of PGC for the testing data were reduced to 13.3 and 0.0839.