Drilling fluid optimization for cuttings transport and rate of penetration
Methods and systems are provided that determine at least one fluid parameter for a drilling fluid and a particular drilling operation, wherein the at least one fluid parameter is selected from the group consisting of: i) a first fluid parameter that relates to shear forces that break apart components of the drilling fluid during the particular drilling operation, ii) a second fluid parameter that characterizes mixing of drill cuttings with the drilling fluid during the particular drilling operation, and iii) third and fourth fluid parameters that characterize normal stress in the drilling fluid during the drilling operation. The methods and systems can evaluate one or more of these fluid parameters to determine a drilling fluid formulation that optimizes the drilling fluid for effective transport of drill cuttings. Methods and systems are also provided that evaluate one or more of these fluid parameters to determine operating parameters that optimize a drilling operation for effective transport of drill cuttings using the drilling fluid.
1 . A method for optimizing a drilling operation, the method comprising:
a) on a data processor, determining at least one fluid parameter for a drilling fluid and the drilling operation, wherein the at least one fluid parameter includes:
i) a first fluid parameter that relates to shear forces that break apart components of the drilling fluid during the drilling operation,
ii) a second fluid parameter that characterizes mixing of drill cuttings with the drilling fluid during the drilling operation, wherein the second fluid parameter represents a dimensionless mixing number based on combination of a Froude number and a Shields number for the drilling fluid and the drill cuttings, and
iii) a transport efficiency metric that characterizes transport of the drill cuttings by the drilling fluid during the drilling operation, wherein the transport efficiency metric is determined from the second fluid parameter in combination with a settling factor calculated from the first fluid parameter, wherein the settling factor is calculated from equations of the form:
L
*
=
L
h
=
u
0
9
η
(
γ
.
)
d
a
(
M
n
)
2
a
3
(
ρ
s
-
ρ
f
)
g
,
d
a
=
2
(
a
+
δ
)
d
a
(
Mn
)
=
{
2
a
Mn
,
Mn
<
1
2
a
,
Mn
≥
1
where u 0 is derived from operational parameters of the drilling operation,
γ is derived from operational parameters of the drilling operation,
M n is a Mason number for the drilling fluid and the drilling operation,
α is a characteristic radius of the drill cuttings,
δ is an accreted gel thickness,
ρ s is a density of the drill cuttings,
ρ f is a fluid density of the drilling fluid, and
g is a gravitational constant;
b) performing multiple iterations of the determining of a) for varying drilling fluid formulations or varying operational parameters of the drilling operation and evaluating at least the transport efficiency metric of iii) for the multiple iterations to optimize a drilling fluid formulation for the drilling operation or at least one operational parameter of the drilling operation; and
c) using the drilling fluid formulation or the at least one operational parameter optimized in b) in the drilling operation.
2 . A method according to claim 1 , wherein:
the first fluid parameter represents the Mason number or a critical shear rate based on the Mason number.
3 . A method according to claim 1 , wherein:
the first fluid parameter represents the Mason number, the Mason number based on a shear rate calculated from at least one operational parameter of the drilling operation selected from the group consisting of: drill pipe radius, drilled borehole radius, angular velocity of a drill string/drill bit, and drilling fluid flow rate.
4 . A method according to claim 3 , wherein:
the drilling fluid comprises an oil-based mud; and
the first fluid parameter represents the Mason number calculated from a mathematical equation of the form
M
n
=
1
2
π
η
0
ϕ
2
G
1
0
σ
y
2
(
ε
r
)
γ
˙
,
where Mn is the Mason number,
η 0 is a fluid viscosity of a continuous phase in the drilling fluid,
Φ is a volume fraction of a dispersed phase in the drilling fluid,
G 10 is a short time elastic modulus (at 10-second sample age) of the drilling fluid,
σ y is a dynamic yield stress of the drilling fluid,
ε is a range of an interaction potential for the drilling fluid,
r is a size of the dispersed phase in the drilling fluid, and
γ is the shear rate of the drilling fluid.
5 . A method according to claim 3 , wherein:
the drilling fluid comprises a water-based mud; and
the first fluid parameter represents the Mason number calculated from a mathematical equation of the form
M
n
=
K
γ
.
G
,
where Mn is the Mason number,
K is a plastic viscosity of the drilling fluid,
G is a short time elastic modulus (at 10-second sample age) of the drilling fluid, and
γ is the shear rate of the drilling fluid.
6 . A method according to claim 1 , wherein:
the drilling fluid comprises an oil-based mud; and
the first fluid parameter represents a critical shear rate determined from flow curve measurements of the drilling fluid performed by an automated rheometer.
7 . A method according to claim 1 , wherein:
the second fluid parameter represents a dimensionless mixing number calculated from a mathematical equation of the form
Ξ
=
(
ρ
f
ω
R
i
H
n
η
H
R
i
+
1
)
3
2
(
ρ
s
-
ρ
f
)
g
a
η
R
i
ω
H
,
where E is the dimensionless mixing number based on the combination of a Froude number and a Shields number for the drilling fluid and the drill cuttings,
ρ s is the characteristic density of the drill cuttings,
ρ f is the fluid density of the drilling fluid,
α is the characteristic radius of the drill cuttings,
R i is a radius of a drilled borehole,
ω is an angular velocity of a drill string/drill bit,
η is a viscosity of the drilling fluid at a desired shear rate,
H is a gap between a drill pipe and the drilled borehole,
g is the gravitational constant, and
n is an arbitrary scale factor.
8 . A method according to claim 1 , wherein:
the at least one fluid parameter of a) further includes a third fluid parameter and a fourth fluid parameter that characterize normal stress in the drilling fluid during the drilling operation;
the third fluid parameter represents a first normal stress coefficient ψ 1 of the drilling fluid or an N 1 stress difference of the drilling fluid; and
the fourth fluid parameter represents a second normal stress coefficient ψ 2 of the drilling fluid or an N 2 stress difference of the drilling fluid.
9 . A method according to claim 1 , wherein:
the evaluating of b) optimizes the drilling fluid formulation for the drilling operation by evaluating the transport efficiency metric of iii) for the varying drilling fluid formulations.
10 . A method according to claim 9 , wherein:
the varying drilling fluid formulations include one or more polymer additives.
11 . A method according to claim 1 , wherein:
the evaluating of b) optimizes the at least one operational parameter for the drilling operation by evaluating the transport efficiency metric of iii) for the varying operational parameters of the drilling operation.
12 . A method according to claim 11 , wherein:
the varying operational parameters of the drilling operation are selected from the group including drill bit/hole size, drill pipe size, drilling fluid flow rate, and/or rotational speed of a drill string.