US 7,063,147 B2 · Method and apparatus and program storage device for front tracking in hydraulic fracturing simulators

Abstract

A method and system and program storage device is adapted to continuously update a perimeter of a fracture footprint created in an Earth formation when a fracturing fluid fractures the formation penetrated by a wellbore. Two embodiments of a Volume of Fluid (VOF) software, adapted to be stored in a memory of a computer system, will locate the position of a fracture perimeter during the evolution of that fracture when the software is executed by the processor of the computer system. The two embodiments, called the ‘Marker VOF (MVOF)’ and the ‘Full VOF (FVOF)’ software, will continuously update the perimeter of the fracture footprint by updating a Fill Fraction for each tip element. The MVOF software will use a fill fraction mass balance integral equation to update the Fill Fraction for each tip element, and the FVOF software will use an integrated form of fluid flow equations to update the Fill Fraction for each tip element.

Claims15

Dependent claims

A method of continuously updating a perimeter of a fracture footprint, said fracture footprint having a plurality of tip elements, comprising the steps of:

(a) updating a fill fraction for each tip clement of said plurality of tip elements by using the following equation:
w
k
+
1
⁢
F
k
+
1
(
j
+
1
)
=
w
k
⁢
F
k
-
Δ
⁢
⁢
t
k
A
e
⁢
∫
Γ
e
⁡
(
t
)
⁢
v
_
k
+
1
(
j
)
·
n
_
⁢
ⅆ
l
-
G
e
⁡
(
F
k
+
1
(
j
+
1
)
,
t
,
t
0
e
)
wherein wk is the fracture width at time tk, wk+1 is the fracture width at time tk+1, Fk is the fill fraction at time tk, Fk+1(j+1) is the fill fraction at time tk+1 and iteration (j+1), Δtk is the time step at time tk, n is the local unit normal to the fracture boundary, Γe(t), at tip element a and time t, vk+1(j) is the local fluid front velocity at time tk+1 and iteration (f), Ge(Fk+1(j+1),t,t0e) is an integrated sink (or leakoff) term over the possibly partially filled tip element e, t0e is the trigger time at which the fluid first enters tip element e, t is the current time, and Ae is the area of the rectangular tip element e.

71 more elements

(a) updating a fill fraction for each tip element of said plurality of tip elements by using the following equation:
w
k
+
1
⁢
F
k
+
1
(
j
+
1
)
=
w
k
⁢
F
k
-
Δ
⁢
⁢
t
k
A
e
⁢
∫
Γ
e
⁡
(
t
)
⁢
v
_
k
+
1
(
j
)
·
n
_
⁢
ⅆ
l
-
G
e
⁡
(
F
k
+
1
(
j
+
1
)
,
t
,
t
0
e
)
wherein wk is the fracture width at time tk, wk+1 is the fracture width at time tk+1, Fk is the fill fraction at time tk, Fk+1(j+1) is the fill fraction at time tk+1 and iteration (j+1), Δtk is the time step at time tk, n is the local unit normal to the fracture boundary, Γe(t), at tip element a and time t, vk+1(j) is the local fluid front velocity at time tk+1 and iteration (f), Ge(Fk+1(j+1),t,t0e) is an integrated sink (or leakoff) term over the possibly partially filled tip element e, t0e is the trigger time at which the fluid first enters tip element e, t is the current time, and Ae is the area of the rectangular tip element e.

71 more elements

A method adapted fir continuously updating a perimeter of a fracture footprint created in an Earth formation when a fracturing fluid fractures the formation penetrated by a wellbore, a mesh overlaying the fracture footprint defining a plurality of tip elements, comprising the steps of:

(a) receiving input data including an old fill fraction F1 associated with the tip elements at an old time step ‘t1’, an old pressure ‘p1’ associated with the tip elements at the old time step, and an old width ‘w1’ associated with the tip elements at the old time step;
(b) incrementing the old time ‘t1’ to anew time step ‘t2’;
(c) solving for a new width ‘w2’ and a new pressure ‘p2’ associated with the tip elements at the new time step ‘t2’ in response to the input data;
(d) solving for a current new fill fraction ‘F2’ associated with the tip elements at the new time step ‘t2’ by using the following equation:
w
k
+
1
⁢
F
k
+
1
(
j
+
1
)
=
w
k
⁢
F
k
-
Δ
⁢
⁢
t
k
A
e
⁢
∫
Γ
e
⁡
(
t
)
⁢
v
_
k
+
1
(
j
)
·
n
_
⁢
⁢
ⅆ
l
-
G
e
⁡
(
F
k
+
1
(
j
+
1
)
,
t
,
t
0
e
)
wherein wk is the fracture width at time tk, wk+1 is the fracture width at time tk+1, Fk is the fill fraction at time tk, Fk+1(j+1) is the fill fraction at time tk+1 and iteration (j+1), Δtk is the time step at time tk, n is the local unit normal to the fracture boundary, Γe(t), at tip element a and time t, vk+1(j) is the local fluid front velocity at time tk+1 and iteration (f), Ge(Fk+1(j+1),t,t0e) is an integrated sink (or leakoff) term over the possibly partially filled tip element e, t0e is the trigger time at which the fluid first enters tip element e, t is the current time, and Ae is the area of the rectangular tip element e;
(a) iterating the above equation by updating the current new fill fraction ‘F2’ (iteration ‘j’) to determine a latest new fill fraction ‘F2’ (iteration ‘j+1’) in response to a latest new value of ‘w2’ (iteration ‘j+1’) and a latest new value of ‘p2’ (iteration ‘j+1’),
(f) determining if the difference between the latest new fill fraction ‘F2’ (iteration ‘j+1’) and the current new fill fraction ‘F2’ (iteration ‘j’) is less than a particular tolerance;
(g) repeating steps (e) and (f) when the difference between the latest new fill fraction ‘F2’ (iteration ‘j+1’) and the current new fill fraction ‘F2’ (iteration ‘j’) is not less than the particular tolerance;
and
(h) when the difference between the latest new fill fraction ‘F2’ (iteration ‘j+1’) and the current new fill fraction ‘F2’ (iteration ‘j’) is less than the particular tolerance, proceed to the next time step ‘t3’ and repeat steps (a) through (g), where time ‘t2’ replaces time ‘t1’ and time ‘t3’ replaces time ‘t2’, and similarly for width and pressure values where width ‘w2’ replaces width ‘w1’, pressure ‘p2’ replaces pressure ‘p1’, and width ‘w3’ replaces width ‘w2’, pressure ‘p3’ replaces pressure ‘p2’.

80 more elements

A program storage device readable by a machine storing a set of instructions executable by the machine to perform method steps for continuously updating a perimeter of a fracture footprint created in an Earth formation when a fracturing fluid fractures the formation penetrated by a wellbore, a mesh overlaying the fracture footprint defining a plurality of tip elements, said method step comprising:

(a) receiving input data including an old fill fraction F1 associated with the tip elements at an old time step ‘t1’, an old pressure ‘p1’ associated with the tip elements at the old time step, and an old width ‘w1’ associated with the tip elements at the old time step;
(b) incrementing the old time ‘t1’ to a new time step ‘t2’;
(c) solving for a new width ‘w2’ and a new pressure ‘p2’ associated with the tip elements at the new time step ‘t2’ in response to the input data;
(d) solving for a current new fill fraction ‘F2’ associated with the tip elements at the new time step ‘t2’ by using the following equation:
w
k
+
1
⁢
F
k
+
1
(
j
+
1
)
=
w
k
⁢
F
k
-
Δ
⁢
⁢
t
k
A
e
⁢
∫
Γ
e
⁡
(
t
)
⁢
v
_
k
+
1
(
j
)
·
n
_
⁢
⁢
ⅆ
l
-
G
e
⁡
(
F
k
+
1
(
j
+
1
)
,
t
,
t
0
e
)
wherein wk is the fracture width at time tk, wk+1 is the fracture width at time tk+1, Fk is the fill fraction at time tk, Fk+1(j+1) is the fill fraction at time tk+1 and iteration (j+1), Δtk is the time step at time tk, n is the local unit normal to the fracture boundary, Γe(t), at tip element a and time t, vk+1(j) is the local fluid front velocity at time tk+1 and iteration (f), Ge(Fk+1(j+1),t,t0e) is an integrated sink (or leakoff) term over the possibly partially filled tip element e, t0e is the trigger time at which the fluid first enters tip element e, t is the current time, and Ae is the area of the rectangular tip element e;
(e) iterating the above equation by updating the current new fill fraction ‘F2’ (iteration ‘j’) to determine a latest new fill fraction ‘F2’ (iteration ‘j+1’) in response to a latest new value of ‘w2’ (iteration ‘j+1’) and a latest new value of ‘p2’ (iteration ‘j+1’), (f) determining if the difference between the latest new fill fraction ‘F2’ (iteration ‘j+1’) and the current new fill fraction ‘F2’ (iteration ‘j’) is less than a particular tolerance;
(g) repeating steps (e) and (f) when the difference between the latest new fill fraction ‘F2’ (iteration ‘j+1’) and the current new fill fraction ‘F2’ (iteration ‘j’) is not less than the particular tolerance;
and
(h) when the difference between the latest new fill fraction ‘F2’ (iteration ‘j+1’) and the current new fill fraction ‘F2’ (iteration ‘j’) is less than the particular tolerance, proceed to the next time step ‘t3’ and repeat steps (a) through (g), where time ‘t2’ replaces time ‘t1’ and time ‘t3’ replaces time ‘t2’, and similarly for width and pressure values where width ‘w2’ replaces width ‘w1’, pressure ‘p2’ replaces pressure ‘p1’, and width ‘w3’ replaces width ‘w2’, pressure ‘p3’ replaces pressure ‘p2’.

79 more elements

Dependencies are inferred from the claim text.

Method and apparatus and program storage device for front tracking in hydraulic fracturing simulators

Life of this patent

Method and apparatus and program storage device for front tracking in hydraulic fracturing simulators

Life of this patent

Abstract

Claims15