Question

A well was drilled to 3000 meters depth with a casing of (9 5/8 inches) nine and five eigths inches with an internal diameter of 6,69 inches, they continued drilling up to 4800 meters obtaining a diameter of 6.7 inches average. Before finishing the drilling they made a test with a drill pipe of (5 1/2 inches) five and a half inches long with a diameter of 4,78 inches until the bottom of the well.
If we consider that the pump used for the job it's a triplex pump, calculate the returning time of the drill pipe that the test was made with.

A well was drilled to 3000 mts depth with a casing of 9 5/8 inches outer diameter and an inner díameter of 6,69 inches, they continued drilling up to 4800 mts obtaining an average hole diameter of 6,70 inches .
Before finishing the drill hole, they sent down the Casing a set of drill pipes with a Tricone . The drill pipes measured 5 1/2 inches outer diameter and an inner diameter of
4 7/8 inches.
Taking into account that the water pump used for the job is a triplex pump, calculate the time for the return of water when the pump efficiency is 0,94 with a cylinder length of 7,5 inches and a displacement 4 gallons/stroke and 30 strokes/ minutes

Answer 1

problem seems typical but it is easy one.

lets start with basics

assumption=water is going to flow through drill casing which they have inserted in well casing before finishing.

(as water flow path is not mentioned in problem)

theory of solution= we need to calculate total time of water output,we can proceed in manner total volume of casing of well divided by flow rate of output of pump.in this manner we can get total time taken by pump to supply water whose volume is equal to Volume of well casing.

lets start calculation part now

volume of well casing in which water is flowing=volume of water= (22/7)h r²=pie multiply height multiply square of radius (mean radius)

need to convert units inch=0.0254mtr

mean diameter of drill pipe=5.1875inch=0.1317625mtr

hence radius =0.06588125 mtr

length=[/]

total volume of drill casing through which water is going it' return=(22/7)*(0.06588125)² 4800=65.45077m³

now

volume rate out by pump=4gallon per stroke

we have 30stroke per minute

so 4*30 gallon per minute=120gallon per minute

unit convertin needed 1gallon=0.00454609 m³

so pump output is 120*0.00454609=0.5455308m³ per minute

now use simple mathematics

time takenby water to return = total volume/vol Output rate by pump

t=65.45077/0.5455308

=119.9763min

so

as problem does not stated flow path of water return also they didn't specified purpose of using triplex pump's data soour answer is 119.97min assuming water flows through drill casing which is very narrow but having significant length.