Page 310 - Fundamentals of Gas Shale Reservoirs

290 PERFORMANCE ANALYSIS OF UNCONVENTIONAL SHALE RESERVOIRS

where additional data, which are necessary for rate‐transient
analysis.
M t k f ,eff t (13.37) Assuming all 18 stages contribute to flow, the analysis of
t o w g (13.38) the straight‐line slope of the rate‐normalized pressure versus
square root of time (Eq. 13.35 and Fig. 13.6) yields 0.002
Equation 13.35 is the solution of Equation 13.39 for a
horizontal well in oil‐producing unconventional reservoirs mD for permeability to oil in the first 6 months of production
with the well configuration presented by Figure 13.1. and 0.0015 mD during the second year of production.
Similarly, Equation 13.36 is the solution of Equation 13.40 However, if only nine stages contribute significantly to oil
for gas‐condensate reservoirs. production, then the calculated oil permeability is 0.008 mD
for the first six months and 0.006 mD during the second year
p of production when gas–oil ratio becomes significantly
k t p o Bq ˆ Bq ˆ Bq ˆ c t o (13.39)
w w
g g
o o
t greater than the solution gas–oil ratio. Core plug absolute
p permeability for this reservoir is of the order of 0.00002
k p Bq ˆ B 380 q ˆ Bq ˆ c o mD. Comparing core and well test permeability reveals that
w w
o
t
gg
oo
t
g
t the formation stimulation has created high‐permeability
(13.40) channels (or macrofractures) in the drainage volume of
the hydraulic fractures. This high‐permeability region is
In Equation 13.40, the coefficient 380 represents the SCF
of gas per pound‐mole of condensate, ξ in molar density in designated as SRV.
Analysis of the straight‐line slope in Figure 13.6 yields a
o
pound‐mole per cubic feet of condensate, q is the cubic feet negative fracture skin factor s face , indicating that the hydraulic
o
hf
of condensate produced, and ˆ q is the specific production fracture surface has a larger permeability than the greater
o
rate of condensate per unit rock volume. SRV region. This is consistent with geomechanical reasoning
For an oil reservoir, the total compressibility is that macrofractures are wider near the hydraulic fracture sur-
c t c S c S c S c (13.41) face than far away.
gg
o oa
wwa
where Figure 13.7 presents the plot of the rate‐normalized pressure
4
versus t for bilinear flow analysis. The analysis of the straight‐
1
c (13.42) line segment on the figure yields k w λ = 52 mD‐ft/cp.
f,eff
hf t
p o
B R 13.4.3.2 Example 2: A Long Pressure Build-up Test
c wa c ˆ w g sw (13.43) Figure 13.8 shows 10 days of pressure buildup in a Bakken
B w p o open‐hole well. This well was stimulated in such a way to
B R create only an axial hydraulic fracture (Kurtoglu, 2013). The
c oa c ˆ o g so (13.44)
B o p o analysis of the test produces effective fracture permeability
of 0.023 mD if we assume that the well effective length is
1 B 50%, Figure 13.9.
ˆ c o (13.45)
o B p
o o
1 B 13.4.4 Type-Curve Matching
c g g (13.46)
B g p o Classic type‐curve matching models pertain to radial flow in
vertical wells producing from high‐permeability conven-
For a gas‐condensate reservoir, total compressibility is: tional reservoirs where the BDF prevails soon after a well
begins to produce. However, type‐curve matching in uncon-
c c Sc Sc Sc (13.47)
t ww oo gg ventional reservoirs must address both transient and BDF in
We have provided additional equations in the Appendix low‐permeability reservoirs, which produce from multistage
to provide more clarity to multi‐phase flow equations. hydraulic fractures in horizontal wells. An appropriate type‐
curve, covering a broad range of variables, might be too over-
whelming. On the other hand, because of the flexibility of
13.4.3 Field Applications
reservoir models, we can use these to assess well performance.
13.4.3.1 Example 1: Rate Transient Analysis Figure 13.5 Reservoir modeling is extremely useful for simulating
presents the production history of an oil well in Eagle the primary production and EOR in shale formations under
Ford formation. This production history is a plot of various operating conditions. However, the selection of
the rate‐normalized pressure versus production time. The the appropriate reservoir model and input data is crucial. For
well was stimulated with 18 fracture stages, and each stage instance, for shale reservoir applications, we believe that
consisted of six clusters. On the figure, we have presented dual‐porosity compositional modeling is most appropriate.