Determination of the optimal fluid pulses for enhancement of reservoir permeability and productivity
View Patent ↗A method of oscillating a pressure in a borehole is provided that includes determining a hydraulic diffusivity, using injection tests, in a borehole, calculating a pressure field using an appropriately programmed computer at a proximal distance to the borehole using a first forced oscillation result in a porous media, calculating a flow rate at the proximal distance from the borehole by multiplying a gradient of the pressure field by a measured permeability and dividing by a viscosity of a fluid under test, computing, using the appropriately programmed computer, a volumetrically averaged flow rate by integrating a square of the flow rate over a volume around the borehole, outputting a value of an angular frequency for which the volumetrically-averaged flow rate is maximum, and operating a pump at a second forced oscillation according to the angular frequency on the fluid under test, where a change in permeability around the borehole is provided.
1. A method of oscillating a pressure in a borehole, comprising:
a) determining a hydraulic diffusivity, using injection tests, in a borehole;
b) calculating a pressure field, using an algorithm programmed in a computer, at a proximal distance to said borehole using a first pressure oscillation result in a porous media;
c) calculating a flow rate, using said algorithm programmed in said programmed computer, at said proximal distance from said borehole by multiplying a gradient of said pressure field by a measured permeability and dividing by a viscosity of a fluid under test;
d) computing, using said algorithm programmed in said computer, a volumetrically averaged flow rate by integrating a square of said flow rate over a volume around said borehole;
e) outputting a value of an angular frequency for which said volumetrically-averaged flow rate is maximum; and
f) operating a pump at a second said pressure oscillation according to said angular frequency on said fluid under test, wherein an increase in permeability around said borehole is provided.
2. The method according to claim 1 , wherein said pressure field in a porous media is calculated according to
p
(
r
)
=
ɛ
[
1
+
C
2
(
1
-
C
2
K
0
(
s
w
)
)
K
0
(
s
)
]
,
wherein p(r) is the pressure at a distance r from said borehole, ε is an imposed oscillation amplitude, K 0 is a modified Bessel function of the second kind of order 0, s is a parameter based on frequency such that
s
=
i
ω
κ
r
.
κ is the hydraulic diffusivity, i is the square root of −1, ω is the angular frequency in radians, and s w is the value of s at a radius of said borehole, wherein C 2 is a constant having a relation
C
2
=
-
r
w
i
ω
2
TK
1
(
s
w
)
κ
i
ω
where T is a hydraulic transmissivity, K 1 is a modified Bessel function of order 1 and r w is the radius of said borehole.
3. The method according to claim 1 , wherein a frequency that maximizes said flow rate at a distance that is selected to dislodge a particular blockage.
4. The method according to claim 1 , wherein said borehole comprises a well or a fracture.