Formation fracture characterization from post shut-in acoustics and pressure decay using a 3 segment model
A method for determining properties of hydraulic fractures from measurements of pressure in a well made after stopping pumping fracturing fluid into the well (shut in) includes determining a first time after shut in whereinafter a decrease in measured pressure is caused by fluid leak off in a fracture. A second time after shut in is determined whereinafter the decrease in pressure is caused by fluid leak off, fracture growth and fluid pressure equilibration in the fracture. A third time after shut in is determined whereinafter the decrease in pressure is caused by fluid leak off, fracture growth, fluid pressure equilibration in the fracture and pressure drop in a near wellbore zone. Values of fluid efficiency, minimum stress and net pressure which are determined result in a calculated pressure with respect to time matching the pressure measurements within a predetermined threshold.
1 . A method for determining properties of hydraulic fractures from measurements of pressure in a well made after stopping pumping fracturing fluid into the well (shut in), comprising:
determining a first time after shut in where after a decrease in measured pressure is caused by fluid leak off in a fracture;
determining a second time after shut in where after the decrease in pressure is caused by fluid leak off, fracture growth and fluid pressure equilibration in the fracture;
determining a third time after shut in where after the decrease in pressure is caused by fluid leak off, fracture growth, fluid pressure equilibration in the fracture and pressure drop in a near wellbore zone; and
determining values of fluid efficiency, minimum stress and net pressure which result in a calculated pressure with respect to time matching the pressure measurements within a predetermined threshold, wherein calculating pressure with respect to time is based on causes of pressure drop in segments corresponding to time between (i) the third time and the second time, (ii) the second time and the first time, and (iii) after the first time.
2 . The method of claim 1 wherein the calculated pressure beginning at the first time comprises calculating Carter leak off.
3 . The method of claim 1 wherein the calculated pressure beginning at the second time and ending at the third time comprises calculating
p
av
=
S
min
+
p
*
+
(
p
n
_
0
-
p
*
)
1
-
ξ
f
ξ
f
tg
[
arctan
(
ξ
f
1
-
ξ
f
)
-
t
t
inj
p
n
_
0
p
n
_
0
-
p
*
ξ
f
(
1
-
ξ
f
)
η
av
]
in which ξ f =Local efficiency or fracture growth ratio at shut-in, η av =Average efficiency from start of fluid pumping to shut in, p av =average net pressure in the fracture, p*=fracture propagation pressure, p n =average net pressure, p n 0 =initial net pressure t inj =injection time, t=time for which pressure calculation is made, and Smin—minimum principal stress.
4 . The method of claim 1 wherein the calculated pressure beginning at the third time and ending at the second time comprises calculating a near wellbore pressure drop from Darcy equation flow for an axisymmetric, bi-wing fracture having cylindrical cross-sectional growth.
5 . The method of claim 1 wherein the calculated pressure beginning at the third time and ending at the second time comprises analyzing reflection events in measurements of pressure or pressure time derivative in response to acoustic pulses emitted into the well, the acoustic pulses inducing tube waves in the well to determine a near field conductivity index to constrain calculation of near wellbore pressure drop.
6 . The method of claim 1 wherein the third time is determined after an end of water hammer induced by the stopping pumping.
7 . The method of claim 1 wherein the second time is determined when a rate of change of the measurements of pressure with respect to time falls below a predetermined threshold.
8 . The method of claim 1 wherein the first time is determined when the measurements of pressure fall below a fracturing pressure of a rock formation into which the fracturing fluid is pumped.
9 . The method of claim 1 further comprising estimating a fluid pressure in a formation penetrated by the fracture using the determined minimum stress.
10 . The method of claim 1 wherein the efficiency comprises a fraction of a volume of the fracture with respect to a volume of fracturing fluid pumped into the fracture.
11 . The method of claim 1 further comprising changing at least one of viscosity of the fracturing fluid, pumped volume of the fracturing fluid, a volume rate of pumping the fracturing fluid, or a concentration of proppant in the fracturing fluid for pumping fracture fluid into a different stage in the well or in a different well.
12 . The method of claim 1 further comprising determining fracture conductivity with respect to time after shut in.
13 . The method of claim 12 further comprising determining a proppant packed conductivity when the fracture conductivity stops changing with respect to time after shut in.
14 . The method of claim 1 further comprising:
using the determined values of fluid efficiency, minimum stress and net pressure; and
using values of Young's modulus, Poisson's ratio, viscosity of the fracturing fluid, pumped volume of the fracturing fluid, a volume rate of pumping the fracturing fluid, a number of well perforation clusters through which the fracturing fluid is pumped, determining a length, a width, a height and a leak off parameter of the fracture.
15 . The method of claim 14 wherein the determining length, width and height of the fracture comprises using a Perkins-Kern-Nordgren model of geometry of the fracture.
16 . The method of claim 14 wherein the determined fracture length, fracture width, fracture height and the leak-off parameters are used to estimate a fluid productivity of each fracture treatment stage and the entire well.
17 . A computer program stored in a computer readable medium, the program comprising logic operable to cause a programmable computer to perform actions on measurements of pressure made in a well after stopping pumping (shut in) a fracture treatment into the well, the actions, comprising:
determining a first time after shut in where after a decrease in measured pressure is caused by fluid leak off in a fracture;
determining a second time after shut in where after the decrease in pressure is caused by fluid leak off, fracture growth and fluid pressure equilibration in the fracture;
determining a third time after shut in where after the decrease in pressure is caused by fluid leak off, fracture growth, fluid pressure equilibration in the fracture and pressure drop in a near wellbore zone; and
determining values of fluid efficiency, minimum stress and net pressure which result in a calculated pressure with respect to time matching the pressure measurements within a predetermined threshold, wherein calculating pressure with respect to time is based on causes of pressure drop in segments corresponding to time between (i) the third time and the second time, (ii) the second time and the first time, and (iii) after the first time.
18 . The computer program of claim 17 wherein the calculated pressure beginning at the first time comprises calculating Carter leak off.
19 . The computer program of claim 17 wherein the calculated pressure beginning at the second time and ending at the third time comprises calculating
p
av
=
S
min
+
p
*
+
(
p
n
_
0
-
p
*
)
1
-
ξ
f
ξ
f
tg
[
arctan
(
ξ
f
1
-
ξ
f
)
-
t
t
inj
p
n
_
0
p
n
_
0
-
p
*
ξ
f
(
1
-
ξ
f
)
η
av
]
in which ξ f =Local efficiency or fracture growth ratio at shut-in, η av =Average efficiency from start of fluid pumping to shut in, p av =average net pressure in the fracture, p*=fracture propagation pressure, p n =average net pressure, p n 0 =initial net pressure t inj =injection time, t=time for which pressure calculation is made, and Smin—minimum principal stress.
20 . The computer program of claim 17 wherein the calculated pressure beginning at the third time and ending at the second time comprises calculating a near wellbore pressure drop from Darcy equation flow for an axisymmetric, bi-wing fracture having cylindrical cross-sectional growth.
21 . The computer program of claim 17 wherein the calculated pressure beginning at the third time and ending at the second time comprises analyzing reflection events in measurements of pressure or pressure time derivative in response to acoustic pulses emitted into the well, the acoustic pulses inducing tube waves in the well to determine a near field conductivity index to constrain calculation of near wellbore pressure drop.
22 . The computer program of claim 17 wherein the third time is determined after an end of water hammer induced by the stopping pumping.
23 . The computer program of claim 17 wherein the second time is determined when a rate of change of the measurements of pressure with respect to time falls below a predetermined threshold.
24 . The computer program of claim 17 wherein the first time is determined when the measurements of pressure fall below a fracturing pressure of a rock formation into which the fracturing fluid is pumped.
25 . The computer program of claim 17 further comprising instructions operable to cause the computer to perform estimating a fluid pressure in a formation penetrated by the fracture using the determined minimum stress.
26 . The computer program of claim 17 wherein the efficiency comprises a fraction of a volume of the fracture with respect to a volume of fracturing fluid pumped into the fracture.
27 . The computer program of claim 17 further comprising logic operable to cause the computer to perform changing at least one of viscosity of the fracturing fluid, pumped volume of the fracturing fluid, a volume rate of pumping the fracturing fluid, or a concentration of proppant in the fracturing fluid for pumping fracture fluid into a different stage in the well or in a different well.
28 . The computer program of claim 17 further comprising instructions operable to cause the computer to perform determining fracture conductivity with respect to time after shut in.
29 . The computer program of claim 28 further comprising determining a proppant packed conductivity when the fracture conductivity stops changing with respect to time after shut in.
30 . The computer program of claim 17 wherein the logic further comprises logic operable to cause the computer to perform the acts of:
using the determined values of fluid efficiency, minimum stress and net pressure; and
using values of Young's modulus, Poisson's ratio, viscosity of the fracturing fluid, pumped volume of the fracturing fluid, a volume rate of pumping the fracturing fluid, a number of well perforation clusters through which the fracturing fluid is pumped, determining a length, a width, a height and a leak off parameter of the fracture.
31 . The computer program of claim 30 wherein the determining length, width and height of the fracture comprises using a Perkins-Kern-Nordgren model of geometry of the fracture.
32 . The computer program of claim 30 wherein the determined fracture length, fracture width, fracture height and the leak-off parameters are used to estimate a fluid productivity of each fracture treatment stage and the entire well.