Pipe Diameter Calculation in $2-$Phase Flow

Calculate the pipe ID required, with the following parameters:

Schedule $40$ piping

Approx. pressure drop $=0\mathrm{.}5$ psi$/100$ ft$.$ or $3\mathrm{.}5$ kPa $/30$ m

Oil flow: $2,000$ m$3/$d $($actual$),$ SG $=0\mathrm{.}9,$ oil viscosity $=50$ cP

Water flow: $6,000$ m$3/$d $($actual$),$ SG$=1\mathrm{.}0,$ water viscosity $=0\mathrm{.}7$ cP

Gas flow: $40,000$ Sm$3/$d $($wet basis$),$ MW$=25,$ gas viscosity$=0\mathrm{.}012$ cP$,$

compressibility Z $=1\mathrm{.}0$

Pressure $=500$ kPag, T $=50$ C

Use the homogeneous flow model.

Suggest to start with the assumption of $12$ NPS pipe