An accurate prediction of Liquid Hold-up and pressure drop in multiphase flow is required in designing of million or billion dollars surface and subsurface facilities projects in Petroleum industries. These projects include building of offshore Oil and Gas pipelines, Oil and Gas field's process plants, multiphase separators, Oil and Gas wells equipments such as tubing, completion equipments. Therefore accuracy in prediction of Liquid Holdup and Pressure drop has a lot of importance and one of most primarily concerns in petroleum and chemical industries.

Beggs and Brill multiphase flow correlation is one of the most widely used multiphase flow correlations in the industry [19] due to its applicability for horizontal, vertical and inclined multiphase flow modeling. It also takes into account the different horizontal and vertical flow regimes. [4] It uses the general mechanical energy balance and the average in-situ density to calculate the pressure gradient. But due to the complex flow regimes and its wide transition, the method prediction becomes poor in certain practical conditions especially, when flow pattern classification parameters are near to the boundaries of the flow regime limits usually due to the inaccurate prediction of slip liquid hold-up. [18]

In this paper modification to Beggs and Brill correlation is proposed by predicting horizontal pipe flow regime using fuzzy logic instead of the one presented by the correlation. A fuzzy model is designed and tested to predict horizontal pipe flow regime and used in Beggs and Brill Correlation. The fuzzy model developed in this study is made by the technique of "Learning from example", which is basically used for rule base construction in automated methods for fuzzy systems [3]. For this purpose the fuzzy logic toolbox of MATLAB is used [17]. In this new proposed method, mixture Froude number and no slip liquid hold up, which were used by Beggs and Brill correlation for flow pattern calculation, are fuzzified. By using these parameters, the coefficients for liquid holdup calculations in Beggs and Brill correlation are modified and eventually produced by this fuzzy model. The new proposed correlation was verified using sets of published data in [1], [2] to predict flow pattern from no-slip holdup and Froude number. Some datasets in [1] were used to further refine the given fuzzy model, particularly high Distributed and low segregated flow regimes, which were not captured by Beggs and Brill data set.

This new proposed fuzzy model indicated that the generated fuzzy model empirical coefficients improve the liquid hold up prediction, which can improve pressure drop prediction of Beggs and Brill correlation; hence improve the accuracy of this widely used multiphase flow correlation. This fuzzy model outperforms the published models and Beggs and Brill multiphase correlation in terms of the lowest absolute average percent error 12.55 % and 9.94 % for Dataset in [1] and [2] respectively.

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