US 11,377,951 B2 · Intelligent water invasion tracking and early warning method for water-gas reservoirs

Abstract

An intelligent water invasion tracking and early warning method for water-gas reservoirs includes based on the gas-water two-phase seepage equation, obtaining the water invasion constant and the water flooding index by combining the gas-water two-phase permeability expression with the water invasion material balance method, fitting by automatic fitting method, finding a best fitting between an optimal theoretical value and an actual value, dividing a block into different water invasion areas based on the water flooding index, revising a water invasion classification boundary based on production dynamic monitoring and well logging interpretation results, and tracking and early warning water invasion by drawing a water flooding index distribution map of water-gas reservoirs according to the water flooding index. The present invention solves the problem of no method for tracking and predicting the water invasion direction and the water invasion intensity in real time.

An intelligent water invasion tracking and early warning method for water-gas reservoirs, the method comprising steps of:

(A) deriving a material balance equation which considers water-sealed gas phenomenon, which comprises:
(A1) establishing a physical model of the water-gas reservoirs which considers the water-sealed gas phenomenon;
(A2) calculating an invasive water quantity in a high permeability area, an invasive water quantity in a low permeability area, a total invasive water quantity, a sealing water quantity, and a sealed gas volume respectively by formulas (1) to (5) of
W
H
=
A
H
⁢
K
H
μ
⁢
Δ
⁢
p
Δ
⁢
L
(
1
)
W
L
=
A
L
⁢
K
L
μ
⁢
Δ
⁢
p
Δ
⁢
⁢
L
(
2
)
W
e
=
ω
⁢
⁢
GB
gi
=
R
B
⁢
GB
gi
(
3
)
W
b
=
W
e
⁢
W
H
W
H
+
W
L
=
W
e
⁢
V
+
⁢
K
+
V
+
⁢
K
+
+
1
(
4
)
G
b
=
W
b
V
+
⁢
B
gi
=
W
e
⁢
V
+
⁢
K
+
V
+
⁢
B
gi
⁡
(
V
+
⁢
K
+
+
1
)
,
(
5
)
wherein WH is the invasive water quantity in the high permeability area, AH is cross-sectional area of the high permeability area, KH is permeability of the high permeability area, μ is gas viscosity, Δp/ΔL is pressure drop per unit length, WL is the invasive water quantity in the low permeability area, AL is cross-sectional area of the low permeability area, KL is permeability of the low permeability area, We is the total invasive water quantity, ω is storativity ratio, G is single well controlled reserves, Bgi is original gas volume coefficient, R is recovery percent of reserves, B is water invasion constant, Wb is sealing water quantity, V+ is dimensionless volume ratio, K+ is dimensionless permeability ratio, Gb is sealed gas volume;
and
(A3) substituting the formulas (1) to (5) in the step (A2) into a material balance equation expressed by a formula (6) to obtain the material balance equation considering the water-sealed gas phenomenon expressed by a formula (7), wherein the formulas (6) and (7) are respectively
GB
g
⁢
i
=
(
G
-
G
p
-
G
b
)
⁢
B
g
+
W
e
(
6
)
p
/
Z
p
i
/
Z
i
=
1
-
R
-
A
⁢
R
B
1
-
R
B
,
(
7
)
wherein
B
gi
=
p
sc
⁢
Z
i
⁢
T
/
p
i
⁢
T
sc
,
⁢
B
g
=
p
sc
⁢
ZT
/
pT
sc
,
⁢
R
=
G
p
/
G
,
A
=
(
V
+
⁢
K
+
V
+
⁢
K
+
+
1
)
⁢
1
V
+
,
⁢
V
+
=
V
H
V
L
,
⁢
K
+
=
K
H
K
L
,
here, Gp is cumulative gas production, Bg is gas volume coefficient, Z is deviation factor, Zi is original deviation factor, p is formation pressure, pi is original formation pressure, A is reservoir heterogeneity coefficient, psc is standard pressure and equal to 0.1013 MPa, Tsc is standard temperature and equal to 293.15 K, T is temperature;
(B) based on the material balance equation considering the water-sealed gas phenomenon and a gas well productivity equation, fitting by automatic fitting method, wherein the gas well productivity equation is p2−pwf2=Cqsc+Dqsc2, here, p is formation pressure, pwf is flowing bottomhole pressure, qsc is gas well production per day, C is laminar coefficient, D is turbulent coefficient, target parameters of the fitting are the reservoir heterogeneity coefficient A, the water invasion constant B, the laminar coefficient C, the turbulent coefficient D and the single well controlled reserves G, the fitting comprises:
(B1) calculating the flowing bottomhole pressure pwf through a wellhead pressure of a production gas well;
(B2) providing upper and lower limits of the target parameters, randomly selecting an initial value within the upper and lower limits, expanding a range defined by the upper and lower limits if a calculation result corresponding to the initial value is out of the range by assigning the calculation result to the upper and lower limits, recalculating till the convergence conditions are met, and calculating the gas well production per day qsc based on the formation pressure p, the flowing bottomhole pressure pwf, an initial value of the laminar coefficient C and an initial value of the turbulent coefficient D by the gas well productivity equation;
(B3) obtaining the cumulative gas production Gp by superimposing the gas well production per day qsc, and calculating a formation pressure p for a next iteration cycle based on the cumulative gas production Gp, an initial formation pressure, an initial value of the reservoir heterogeneity coefficient A, an initial value of the water invasion constant B and an initial value of the single well controlled reserves G by the material balance equation considering the water-sealed gas phenomenon;
and
(B4) continuing iteration from the step (B1) through the formation pressure p obtained by the step (B3), wherein one day in production data is an iteration cycle, obtaining the flowing bottomhole pressure, water production and the water invasion constant B during an entire production stage, adjusting parameters in the upper and lower limits, fitting the flowing bottomhole pressure and the water production by automatic fitting method, finding a best fitting between an optimal theoretical value and an actual value of the lowing bottomhole pressure and the water production, wherein a convergence condition for water production fitting is expressed by a formula of
E
=
∑
i
=
1
⁢
[
q
wei
⁡
(
A
,
B
,
C
,
D
,
G
)
-
q
wei
]
2
≤
0.0
⁢
001
,
(
8
)
here, E is deviation, qwci (A, B, C, D, G) is the optimal theoretical value of the water production, qwci is the actual value of the water production;
and
(C) converting the water invasion constant into a water flooding index by a formula of
I
w
=
(
G
p
/
G
)
B
⁢
G
⁢
B
g
+
W
p
⁢
B
w
G
p
⁢
B
g
+
W
p
⁢
B
w
,
(
9
)
wherein Iw is the water flooding index, Wp is cumulative water production;
revising a water invasion classification boundary, and then dividing a block into a non-water invasion area, a weak water invasion area and a strong water invasion area according to a revised water flooding index interval;
and
based on the non-water invasion area, the weak water invasion area and the strong water invasion area, performing a water invasion degree judgment on the water flooding index, thereby achieving tracking and early warning water invasion.

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Intelligent water invasion tracking and early warning method for water-gas reservoirs

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Intelligent water invasion tracking and early warning method for water-gas reservoirs

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Abstract

Claims2