In a well, the vertical depth is 6,615 ft and the well is filled to the top with a incompressible oil of density 48 lbs/ft^3 . The valve has been closed so that all flow has stopped. The pressure gauge (p1) at that point reads 4410 psia. At the bottom end of the long horizontal extension is the entry point of the well. The pipe is plugged with a 10 cm long porous cylinder separating it from the reservoir fluid at pressure p2. The permeability of the plugging material is 100 mD (milli darcy). The vertical piping is 15 cm in diameter, the horizontal piping is 8 cm inner diameter.
a) what is the reservoir pressure p2?
b) assume the valve is opened fully so that under steady state flow, the pressure p1 becomes 14.7 psia. assume the fluid has 5 cp viscosity. what is the flow rate out through the valve?
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