Method, program and computer system for scaling hydrocarbon reservoir model data
A method, program and computer system for changing scale of reservoir model permeabilities (for example a hydrocarbon reservoir) are provided. Mini-models of reservoirs are defined (S 100 ) with a number of meshes and cells in these meshes. For each model mesh, a scaling of the permeability values K H of the meshes is carried out (S 400 - 800 ) via a mean power formula K H ω H ∝Σk H i ω H relating the mesh permeability K H to the local permeabilities k H,i of the cells. According to the invention, the power coefficient ω H appearing therein is analytically modified, relatively to its expression given by the Noetinger-Haas relationship, in order to correct a non-ergodicity bias.
1. A method for scaling data of a reservoir model, the method comprising:
defining a set of models using a computer, each model in the set including meshes with given dimensions, the meshes each including cells;
receiving statistical data relative to porosity and permeability using the computer, the statistical data including laws of porosity and permeability distributions and a variogram defined by correlation lengths L H , L V along two distinct directions H, V, the laws and the variogram being applicable to each model in the set;
assigning, using the computer, cell permeability values k Hi and cell porosity values Φ Hi depending on the statistical data;
scaling, using the computer, a mesh permeability value K H for each of the meshes, based on a mean power formula
K
H
ω
H
∝
∑
k
H
i
ω
H
relating the mesh permeability value K H to the cell permeability values k Hi of the cells via a power coefficient ω H of having a relationship
ω
H
=
Arctan
α
π
-
Arctan
α
,
the power coefficient ω H being analytically modified to correct a non-ergodicity bias due to the given dimensions of a relevant mesh by a non-ergodicity parameter depending on mesh dimensions D H , D V , according to the relationship
ω
H
=
Arctan
α
π
-
Arctan
α
,
wherein
α
=
L
H
L
V
×
k
V
k
H
ɛ
and
k
V
k
H
and
L
H
L
V
designate petrophysical and geostatistical anisotropies of each model in the set, respectively, the anisotropies depending on the statistical data; and
determining, using the computer, reservoir permeability and porosity values based on the set of models, using the scaled mesh permeability values.
2. The method according to claim 1 , wherein the power coefficient ω H is analytically modified by two non-ergodicity parameters V , H relative to two distinct directions H, V, according to the relationship
ω
H
=
Arctan
α
π
-
Arctan
α
,
wherein
α
=
L
H
L
V
k
V
k
H
ɛ
H
,
ɛ
V
.
3. The method according to claim 2 , wherein the two non-ergodicity parameters V , H depend on respective limiting values (D H /L V/H ) loss and (D V /L V ) loss , below which the power coefficient ω H varies substantially.
4. The method according to claim 3 , wherein the two non-ergodicity parameters V , H are also a function of a mean in and a variance σ of the reservoir permeability values the mean m and the variance σ depending on the statistical data.
5. The method according to claim 3 further comprising:
determining distributions of the two non-ergodicity parameters, V , H , for each of the models using an analytical model;
drawing non-ergodicity parameter values from the distributions of the two non-ergodicity parameters to obtain corrected non-ergodicity parameter values; and
determining a distribution of power coefficient values ω H depending on the corrected non-ergodicity parameter values.
6. The method according to claim 5 further comprising:
calculating a mesh porosity value for each of the meshes; and
calculating as many corrected permeability values of each of the meshes as there are drawings of the corrected non-ergodicity parameter values.
7. The method according to claim 6 , wherein the calculated mesh porosity value of each of the meshes involves an arithmetic mean of the cell porosities of the meshes.
8. The method according to claim 5 , wherein more than ten of the non-ergodicity parameter values are drawn for each model in the set.
9. The method according to claim 3 , wherein the two non-ergodicity parameters are expressed as a function
V
/
H
=
f
(
X
V
/
H
)
wherein X V/H depends on the ratio (D H /L V/H ) of a dimension D V/H of the mesh to the correlation lengths and on the limiting value (D H /L V/H ) loss of the ratio, and wherein the function
V
/
H
=
f
(
X
V
/
H
)
satisfies the condition:
Lim
ɛ
V
/
H
→
1
|
(
D
V
/
H
/
L
V
/
H
)
→
(
D
V
/
H
/
L
V
/
H
)
loss
.
10. The method according to claim 9 , wherein
X
V
/
H
=
1
-
(
D
V
/
H
/
L
V
/
H
)
(
D
V
/
H
/
L
V
/
H
)
loss
,
and the function
V
/
H
=
f
(
X
V
/
H
)
is of the polynomial type:
ɛ
V
/
H
=
1
+
∑
i
=
1
…
X
V
/
H
i
.
11. The method according to claim 1 further comprising:
providing a set of local reservoir permeability values k Hi,r and an apparent permeability value K H,r ; and
calculating a power value ω H,r from a mean power formula
K
H
,
r
ω
H
,
r
∝
∑
k
H
,
r
ω
H
,
r
relating the apparent permeability value K H,r to the local reservoir permeability values via the power value ω H,r and the set of local reservoir permeability values k Hi,r and the apparent permeability value K H,r ;
comparing the calculated power value ω H,r with a reference value; and
modifying the the set of local reservoir permeability values k Hi,r the apparent permeability value K H,r depending on the comparing operation.
12. The method according to claim 11 wherein the calculation of the power value ω H,r is based on a relationship
k
ω
H
,
r
/
H
,
r
=
f
(
{
k
ω
H
,
r
/
H
i
,
r
}
i
=
1
,
N
)
from the mean power formula.
13. The method according to claim 11 , wherein the apparent permeability value K H,r is relative to a direction distinct from a direction of a well of the reservoir.
14. The method according to claim 13 , wherein the direction distinct from the direction of the well is perpendicular to the direction of the well.
15. A method comprising:
defining a set of models using a computer, each of the models including meshes having given dimensions, each of the meshes having cells;
receiving statistical data using the computer, the statistical data including laws of porosity and permeability distributions and a variogram defined by correlation lengths along distinct direction;
assigning cell permeability values and cell porosity values depending on the statistical data using the computer;
scaling a mesh permeability value for each of the meshes using the computer, the scaling based on a mean power formula relating the mesh permeability value to the cell permeability values using a power coefficient that is analytically modified to correct a non-ergodicity bias; and
determining reservoir permeability values and reservoir porosity values based on the scaled mesh permeability values using the computer.
16. A computer readable storage medium encoding a computer executable program for executing a process, the process comprising:
defining a set of models using a computer, each of the models including meshes having given dimensions, each of the meshes having cells;
receiving statistical data using the computer, the statistical data including laws of porosity and permeability distributions and a variogram defined by correlation lengths along distinct direction;
assigning cell permeability values and cell porosity values depending on the statistical data using the computer;
scaling a mesh permeability value for each of the meshes using the computer, the scaling based on a mean power formula relating the mesh permeability value to the cell permeability values using a power coefficient that is analytically modified to correct a non-ergodicity bias; and
determining reservoir permeability values and reservoir porosity values based on the scaled mesh permeability values using the computer.