Page 309 - Fundamentals of Gas Shale Reservoirs

FLOW RATE AND PRESSURE TRANSIENT ANALYSIS IN UNCONVENTIONAL RESERVOIRS 289
(a) oil production (b) gas production
1000 10

100 1
q o (STB/D) 100 q g (STB/D)

1 0.1

0.1 0.01
0 200 400 600 800 0 200 400 600 800
Time (day) Time (day)
FIgURE 13.4 Field example 1: Exponential decline trend.

k k k (13.31) The pressure build‐up equation for the dual‐porosity
f,eff f f m bilinear flow regime is
For pressure buildup, the following equation applies:
t
p () p ( t ) 0
wf
ws
p () p ( t ) 0 qB qB qB
t
wf
ws
qB qB qB o o w w g g
o o w w g g
/ 14
/
44 .102 1 (45 .103 ) 1 1 12 1
t
t t t t / 14 () / 14 t
/
hn wk c t k f ,eff p k hn 2 y 1 14
,
hf hf hf fm f eff hf hf 4 k m t 1 c t fm
(13.32) 14
/
t
/
t p t () 14
In practice, one obtains more accurate and reliable results
from a pressure build‐up test—especially if the build‐up test (13.34)
is conducted a few weeks after well cleanup.
13.4.2 Linear Flow Analysis for Reservoir
Permeability
13.4.1.2 Dual-Porosity Bilinear Flow The material pre-
sented in this section is a more elaborate extension of the Rate transient analysis is a practical method to calculate the
previous section. Here, the hierarchy of flow includes flow effective permeability of the SRV volume. The equation we use
from matrix to macrofractures, then linear flow from macro- for RTA is Equation 13.35, which is the solution of the three‐
fractures to the infinite‐conductivity hydraulic fractures and to phase, black‐oil diffusivity equation for the infinite‐acting
the horizontal well. Thus, we deal with three media—matrix, period (i.e., before the outer boundary effects appear). Similarly,
macrofractures, and infinite‐conductivity hydraulic fractures. Equation 13.36 is for the gas‐condensate reservoirs when the
Equation 13.33 presents the intermediate bilinear flow condi- surface oil is the condensate collected in the surface separators.
tions. However, its use is more reliable when used in pressure Oil can also condense in the reservoir to form S ; however, we
o
build‐up tests, which could yield a numerical value for the assume that the condensed oil in the reservoir is not mobile.
dual‐porosity shape factor σ (Torcuk et al., 2013a).
pt()
pt() qB qB qB
o o w w g g
qB qB qB 1/2
/
o o w w g g . 4 064 (13.35)
2 1 t 141 .2 s face
M hny c Mhn hf
1 12
/
(45 .103 ) t 1 1 1 t 14 t hf hf t fm t hf
/
/
k f ,eff hn hf 2 y hf 1 k 1 c 14 pt()
q
4 m t t fm qB w 380 oo q B g
g
w
/
141 2 . 1 12 (13.36)
.
t s well . 4 064 2 1 141 2
k k hn hf t s face
hf
hf
f ,eff
M t hny hf c t Mhn hf
t
hf
(13.33) fm