# PETE 4086 HW 1

```PETE 4086
Spring'18
HOMEWORK 1
Due: Tuesday, Jan. 30, 2018
________________________
Name
PROBLEM 1
Show your understanding of drilling basics - fill in proper terms and check all correct
statements:
A. In vertical wells, fracturing pressure increases with drilling progress;
B. In vertical wells, drilling with the same density mud my cause fracturing;
C.* In vertical wells, ECD increases with drilling progress;
D.* In vertical wells, ECD remains constant with drilling progress;
E.* In horizontal wells, ECD increases with drilling progress;
F.* In horizontal wells, ECD remains constant with drilling progress;
G. In horizontal wells, drilling with the same density mud may cause fracturing;
H. In horizontal wells, fracturing pressure increases with drilling progress;
I. In horizontal wells, fracturing pressure remains constant with drilling progress;
J. Pressure drop across the drill bit represent only converted energy.
________________________________________
* Assume constant pumping rate
PROBLEM 2
A. Drill bit nozzles convert …………… ……….energy to ………….………… energy;
B. Converted energy corresponds to …….…. % of pressure drop across the bit;
C. In horizontal drilling, well ………….. depth increases with drilling progress;
D. In horizontal wells, well ………….. depth remains constant with drilling progress.
PROBLEM 3: Exercise 4.21 (SPE Textbook)
PROBLEM 4: Exercise 4.24 using the following viscometer readings
3
6
100
200
N, rpm
10
11
22
35
ΘN
300
600
50
90
Note: Solve (a), (b), and (c) as is; For (d) and (e), use all readings;
Graduate students: (f) Estimate three coefficients of YPL model, τy, K, and n
PROBLEM 5:
Drilling is performed at 13,000 ft with the downhole hydraulic motor operated just above
the bit. The bit is equipped with two 12/32, and one 14/32 nozzles. A 13 ppg mud is
circulated at the pump rate of 70 spm. The recorded pump pressure is 4000 psi. Other
relevant data is as follows:
Mud pump factor (manufacturer’s table) = 5.4 gps;
Volumetric efficiency measured on site = 0.83;
Frictional pressure losses in the drill string and annulus (at pumping rate 60 spm) are
1000 psi, and 200 psi,
respectively.
Calculate pressure drop and hydraulic horsepower consumption of the downhole motor.
PROBLEM 6: (Extra credit)
You arrive at the rig site when drilling is in progress at the depth 14,000 ft with 13,200 ft
of 5-in drill pipe and 800 ft of 8-in drill collars in 11.5-in wellbore. The company man
wants to know the bottomhole pressure while drilling and size of the nozzles, but there
is no record of nozzle installation. Pumping rate of a 12.3-ppg mud (having plastic
viscosity 14 cP, yield stress 10 lbf/100 sq ft, and 10-min gels 30 lbf/100 sqft) is 300 gpm
and pump pressure is 3400 psi. You get information on drill string geometry and
compute pressure losses inside and outside drill string as 1,400 psi, and 230 psi,
respectively.
A. Calculate the bottomhole pressure and the size of three equal nozzles.
Hint:
Consider well pressure balance (Bernoulli formula 4.29), Point 1 at pump suction; Point 2
@ bottom of annulus, and find bit nozzle velocity, first.
Circulation was stopped for adding a single, which took over 10 minutes due to
complications and the company man wants to know from you the bottomhole pressure
when the pumps are started slowly at 50 gpm.
B. Estimate the minimum and maximum bottomhole pressures during this operation.
```