PETROLEUM ENGINEERING 4045 – DRILLING ENGINEERING
HOMEWORK ASSIGNMENT # 3 -- FALL 2017
Drilling Fluids
1- A 15-in hole is drilled to a depth of 4,000 ft. The API water loss of the mud is 10 mL.
Approximately 30% of t
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PETROLEUM ENGINEERING 4045 – DRILLING ENGINEERING
HOMEWORK ASSIGNMENT # 3 -- FALL 2017
Drilling Fluids
1- A 15-in hole is drilled to a depth of 4,000 ft. The API water loss of the mud is 10 mL.
Approximately 30% of the lithology is permeable sandstone and the rest is
impermeable shale.
a. Construct a plot of estimated filtration loss in barrels vs. time in hours (0 to 24
hours) that would occur if the hole where drilled instantaneously. Assume
porosity is 25% (answer: 42.4 bbl after 24 hr)
30% of permeable sandstone = 0.30 (4,000 ft) = 1,200 ft
Vf = Const. A. √?
From API water loss test: Vf = 10 ml = 62.9.10-6 bbl;
A= 45 cm2 = 48.44.10-3 ft2 and t = 30 min= 0.5 hr
Then: Const = 1.84. 10-3 bbl/ft2/h1/2
For the sandstone area exposed: A = 3.14 (15 in) (1,200) / 12 = 4,712.4 ft2
Then the filtrate volume is:
Vf = 8.671. √? (with this equation we construct the plot asked above)
After 24 hr we will have: Vf = 8.671. √24 = 42.48 bbl
b. Compute the radius of the invaded zone for Part a. in inches after 24 hours.
(answer: 9.62 in)
Porous volume around the well invaded by the filtrate after 24 hours: Vporous
Vporous = (3.14/4).(Dinv2 – Dwell2).L.ϕ = (3.14/4).( Dinv2 – 152).1,200.(0.25)
But, Vporous = Vf = 42.48 bbl
Then: Dinv = 19.26 in = 9.63 in
c. Repeat Part a. assuming a drilling rate of 200 ft/hour. (answer: 31.6 bbl after
24 hr)
Here we must consider the area drilled per hour as: A = Dwell . π. R. t / 12
(where R is the drilling rate)
Substituting in the integral equation (see textbook page 46; equation (2.7), and
integrating, we obtain:
Vf = 1.84. 10-3. π. Dwell. R.√?33 / 12 / √3 = 0.834. √?3
For drilling the sandstone @ 200 ft/h drilling rate it is going to take 6 hours,
then:
Vf (after 6 hours) = 0.834. √63 = 12.16 bbl
For the remaining 18 hs we suppose instantaneously drilling, then:
Vf = 8.671. (√24 - √6 ) = 21.24 bbl
In 24 hours we have: Vf (24 hs) = 12.16 + 21.24 = 33.4 bbl
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