Page 307 - Fundamentals of Gas Shale Reservoirs

FLOW RATE DECLINE ANALYSIS 287
Both equations indicate that the rate‐normalized pressure of SRV for that stage and the change in Stock tank barrel
plot versus t is a line with a positive slope. Please note that (STB) of oil per unit pore volume:
when flow rate is constant, the coefficient (π/2) disappears in
Equation 13.23 (Wattenbarger et. al., 1998). 0 n
Nt t 0 SRV S o S o
p
13.3.2.3 Boundary-Dominated Flow Regime Now we n hf B o B o (13.27)
assess the long‐time behavior of the decline rate equation as
b approaches 1.0 or becomes smaller than 1.0. For this
assessment, we rewrite Equation 13.19 as given below: The superscripts 0 and n refer to the initial time t and
0
time t t .
n
Similarly, for dry gas shale reservoirs, the estimated
b / 1
b / 1
p pbD i t b / 1 pbD i t b / 1 / 1 2 t ultimate recovery (EUR) for gas per hydraulic fracture stage
qt B qB i qB i equals the product of SRV and the standard cubic feet (SCF)
()
i
i
of gas per unit pore volume:
(13.24)
0 n
This equation indicates that the slope of the rate‐normalized Gt t 0 S g S g
p
pressure versus t increases with time, which we observe in n SRV B B (13.28)
field data (Fig. 13.3). The increase in slope is generally a hf g g
response to the outer boundary effects. The flow behavior is
known as boundary‐dominated flow (BDF). Equation 13.27 does not account for the natural gas
Numerical simulation indicates that during BDF, the liquid, nor does Equation 13.28 account for the conden-
value of b approaches 0.001. With such small b, we approx- sate dropping out in the reservoir or in the gas processing
imate the long‐term reservoir performance by the exponential plant. Accounting of these details requires compositional
decline behavior, whose rate exponent b is zero. Thus, we material balance. Equation 13.28 is the material balance
integrated Equation 13.2 from the onset of the boundary equation for production of free gas. To account for total
effect t to any future time t to obtain the cumulative produc- gas production, one must add cumulative produced solu-
2
tion for the (tt ). We obtained: tion gas to the cumulative free gas production. Neither
2
Equation 13.27 nor Equation 13.28 accounts for natural
q
Nt t 2 2 e Dt e Dt 2 (13.25) gas liquids.
22
p
D 2
We also know that the cumulative production N p tt 13.3.3 Field Applications
0
at time t is the sum of cumulative production in the earlier
intervals, shown below: 13.3.3.1 Example 1: Rate Decline Analysis This
example is the production history of an Eagle Ford
Nt t N t t Nt t (13.26) liquid‐rich well. The rate history of the well exhibits
p 0 p 2 0 p 2 three flow regimes: bilinear flow and linear flow fol-
lowed by BDF, as shown in Figure 13.3. Region 1, the
where
bilinear flow regime, shows the flow rate data from the
first practical measurement time t until time t . This flow
Nt 2 t 0 cumulativeproductionfor time interval, t 2 t 0 rate region exhibits –1/4 slope. Region 2, the linear flow
1
0
p
regime, covers the time interval t t and has a slope
1
2
Nt t 2 cumulativeproductionfor time interval, t t 2 of –1/2. We present the bilinear and linear flow analysis
p
in Section 13.5. However, in this section, we will only
Nt t 0 cumulativeproductionfor total time, t t 0 focus on estimating the ultimate cumulative hydrocarbon
p
production.
Equation 13.26 provides a method to estimate the ulti- We calculate the cumulative hydrocarbon production for
mate recovery for the well (as the sum of the measured Region 1 and Region 2 using daily production data in the
cumulative production in the first several months plus the field; however, we calculate the cumulative production for
late‐time extrapolation of the well flow rate). The ultimate Region 3 using exponential decline equation, Equation 13.25
recovery is synonymous with the estimated ultimate (Table 13.1). For exponential decline analysis, we used the
recovery (EUR). oil and gas flow rates reported in Figure 13.4a and b. The
For black oil shale reservoirs, the cumulative produced decline rate D for the oil and gas are 0.0015 and 0.0009
2
oil recovery per hydraulic fracture stage equals the product day , respectively.
–1