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The following ine#ualities are used to determine the flow pattern that would e4ist if the pipe were hori!ontal. The e#uations for the modified flow-pattern transition boundaries are Beggs and Brill chose to correlate flow-pattern transition boundaries with no-slip li#uid holdup and mi4ture "roude number, given by Fr "ig ).1' shows both the original and the modified dashed lines flow-pattern maps. Their original flow-pattern map map has has been been modi modifi fied ed slig slight htly ly to incl includ udee a tran transi siti tion on !one !one betw betwee een n the the segregated- and intermittent-flow patterns.
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3n the basis of observed flow pattern for hori!ontal flow only, the prepared an empirical map to predict flow pattern. ).12 illustrates the hori!ontal-flow pattern considered by Beggs and Brill. Hori!o hori!onta ntall of developed from 5() measured tests.īeggs and Brill proposed the following pressure-gradient-e#uation for inclined pipe. $fter a particular set of flow rates was established, the inclination of the pipe was varied through the range of angles so that the effect of angl anglee on hold holdup up and and pres pressu sure re grad gradie ient nt were were meas measur ured ed at angl angles es from from the the o "or each pipe si!e, li#uid and gas gas rates were varied so that, when the the pipe was hori!ontal, all flow patterns were observed. The pipe could be inclined at any angel from the hori!ontal. Their Their test test facility was 1-and 1.5-in. The Beggs and Brill method was the first one to predict predict flow flow behavi behavior or at all inclin inclinati ation on angels angels, inclu includin ding g direc directio tional nal wells.