Page 262 - Petroleum Production Engineering, A Computer-Assisted Approach

Guo, Boyun / Computer Assited Petroleum Production Engg 0750682701_chap17 Final Proof page 261 3.1.2007 9:19pm Compositor Name: SJoearun

HYDRAULIC FRACTURING 17/261
Fracture height: 100 ft Pad volume:
Fluid injection rate: 40 bpm 1 h 1 0:3875
Final proppant concentration: 3 ppg « ¼ ¼ ¼ 0:44
1 þ h 1 þ 0:3875
4
Assuming KGD fracture, estimate V pad ¼ V inj « ¼ (6:26 10 )0:44ð Þ ¼ 2:76 10 gal
4
a. Fluid volume requirement
It will take 17 min to pump the pad volume at an injection
b. Proppant mixing schedule rate of 40 bpm.
c. Proppant weight requirement b. Proppant mixing schedule:
d. Propped fracture width
t 17 0:44
c p (t) ¼ (3)
Solution 37 17
gives proppant concentration schedule shown in Table
a. Fluid volume requirements: 17.3. Slurry concentration schedule is plotted in Fig. 17.11.
The average fracture width: c. Proppant weight requirement:
" # 1=4
q i m(1 n)x 2 c f 3
p
w w ¼ 0:29 f c c p ¼ 1 þ « ¼ 1 þ 0:44 ¼ 2:08 ppg
Gh f 4
4
4
c
2 3 1=4 M p ¼ c p (V inj V pad ) ¼ (2:08)(6:26 10 2:76 10 )
¼ 0:29 4 (40)(1:5)(1 0:25)(1,000) 2 5 ¼ 0:195 in: ¼ 72,910 lb
(3 10 6 ) (70) 4
2(1þ0:25) d. Propped fracture width:
Fracture area:
M p 72,910 3
5
A f ¼ 2x f h f ¼ 2(1,000)(100) ¼ 2 10 ft 2 C p ¼ ¼ ¼ 0:3645 lb=ft
2x f h f 2(1,000)(100)
Fluid volume based on volume balance: 0:3645
p ffiffiffi w ¼ C p ¼ ¼ 0:00368 ft ¼ 0:04 in:
w
q i t i ¼ A f w þ 2K L C L A f r p t i : (1 f p )r p (1 0:4)(165)
Assuming K L ¼ 1:5,

0:195
5
3
(40)(5:615)t i ¼ (2 10 ) 12 þ 2(1:5)(2 10 ) 17.5.6 Production forecast and NPV Analyses

70 p ffiffiffi The hydraulic fracturing design is finalized on the basis of
production forecast and NPV analyses. The information
5
(2 10 ) t i
100
gives t i ¼ 37 min. Table 17.3 Calculated Slurry Concentration
Check K L value:
t (min) c p (ppg)
4
V inj ¼ q i t ¼ (40)(42)(37) ¼ 6:26 10 gal
0 0
0:195
4
5
w
V frac ¼ A f w ¼ (2 10 ) (7:48) ¼ 2:43 10 gal 17 0.00
12
20 1.30
V frac 2:43 10 4 23 1.77
h ¼ ¼ ¼ 0:3875 26 2.11
V inj 6:26 10 4 29 2.40

1 3 1 3 32 2.64
K L ¼ h þ p(1 h) ¼ (0:3875) þ p(1 0:3875) 35 2.86
2 8 2 8
37 3.00
¼ 1:48 OK
3.5
3.0
Slurry Concentration (ppg) 2.0
2.5
1.5
1.0
0.5
0.0
0 5 10 15 20 25 30 35 40
Injection Time (min)
Figure 17.11 Calculated slurry concentration.