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OCR for page 166
Appendix D
Calculating the Differential Pressure
at the Start of the Negative Test and
the Quality of Foam Cement
See the well diagram in Figure D-1.
8367'
17483' top of spacer
18037' TOC inside casing
18304' end of casing
FIGURE D-1 Well diagram.
1. Pressure differential at the start of the negative test:
166
OCR for page 167
167
Appendix D
p = po – pi
where
p = pressure differential [pounds per square inch (psi)];
po = pressure outside the casing at the bottom (psi), assumed equal to
reservoir pressure of 11,892 psi, which is a pore pressure of 12.57
pounds per gallon (ppg) at the bottom of the reservoir at 18,212 feet
(true vertical depth); and
pi = pressure on the inside above the cement (psi).
0.433
8,367(8.66) 9,116(14.17) 554(14.3) 999 psi
p 11,892
8.33
Here the differential is into the casing. The cement is treated as a solid that does
not transmit hydrostatic pressure but that must be strong enough to withstand the
pressure differential across it. The top of the cement inside the casing is based
on the assumption that 2.8 barrels of foam cement flowed back into the casing
when the pressure was bled off at the end of the cement job.
2. Foam quality calculations:
Foam cement: The purpose in this case is to reduce the bottom hole (in situ)
density of the slurry from 16.74 ppg to 14.5 ppg. The bottom hole pressure is the
hydrostatic pressure of 14 ppg mud or 13,321 pounds per square inch gauge
(psig) at 18,304 feet. The static bottom hole temperature is 245F.
s = 16.74fc + NfN
where
1 = fc + fN,
s = slurry density (lbm/gal),
N = nitrogen density (lbm/gal),
fc = weight fraction of cement base slurry, and
fN = weight fraction of nitrogen.
N p ft 3
13,335.7 lb lb
N 2.7 2.7(0.9672) 28.9 m 3.86 m
3
zT 1.71(705) ft 7.48 gal gal
fN = (14.5 – 16.74)/(–16.74 + 3.86) = 0.174
fc = 0.826
OCR for page 168
168 Macondo Well Deepwater Horizon Blowout
where
N = specific gravity of nitrogen (compared with air),
p = pressure (pounds per square inch absolute),
z = gas deviation factor (dimensionless), and
T = temperature (degrees Rankine = 460 + degrees Fahrenheit).
So, for every in situ gallon of slurry there will be 0.174 gallon of nitrogen
mixed with 0.826 gallon of base 16.74-ppg cement slurry. Thus, the in situ foam
quality is 17.4 percent. Note that the Chevron tests used a 13 percent quality
foam, which corresponds to the weight fraction of nitrogen necessary to create a
14.5 ppg density foam at atmospheric conditions. Therefore, more nitrogen is
required to create the same density foam at the much higher pressure and
temperature of the bottom of the Macondo well.
At the mixer at the surface, the slurry is blended and pumped at about 600
psig. The volume of nitrogen introduced to 0.826 gallons of base cement is the
in situ volume increased through the real gas law.
0.979 520 13,335.7
V600 0.174 1.6 gallons
1.71 614.7 705
This is added to 0.826 gallon of base cement. Thus, for every 1 gallon of base
cement, 1.94 gallons of N2 at 600 psig is required. This is a 66 percent quality
foam.
The density of the foam slurry at the mixer will be as follows:
614.7 lb lb
N 2.7(0.9672) 3.15 m 0.42 m
ft 3
0.979(520) gal
lb m
s 16.74(0.34) 0.42(0.66) 5.97
gal
The previous equations and results can be combined to obtain an equation
for the density of the slurry at any depth with a corresponding pressure,
temperature, and gas deviation factor.
s 16.74(1 f N ) N f N
2.7(0.9672) p p
N 0.349
7.48 Tz Tz
VN
fN
VN 0.826
OCR for page 169
169
Appendix D
Tz 13,335.7 Tz
VN 0.174 1.925
p 1.71(705) p
Tz Tz
1.925 1.925
p
p p
s 16.74 0.349
1
1.925 Tz 0.826 Tz 1.925 Tz 0.826
p p
Tz
Tz Tz
s
1.925 0.826 16.74
1.925 0.826 1.925 0.349(1.925)
p
p p
14.5
s
Tz
1.925 0.826
p
where s, T, p, and z are as previously defined.
