Estimation of pipe friction and stage resistance based on pressure temporal gradient
A method for evaluating one or more properties of a wellbore. The method may include generating a tube wave in a wellbore, measuring a pressure created by the tube wave at a wellhead and creating a time-domain model based at least in part on the pressure. The method may further include identifying a Darcy factor and a stage resistance based at least in part on the time-domain model.
1 . A method comprising:
generating a tube wave in a tubular of a wellbore;
measuring a pressure created by the tube wave at a wellhead;
creating a time-domain model based at least in part on the pressure; and
identifying a Darcy factor, wherein the Darcy factor is found using
α
=
fLQ
0
2
V
w
DA
,
where the α is a pipe friction, f is a friction factor, L is a length of one or more tubulars in the wellbore, Q o is a flow rate, V w is a speed of the tube wave in the tubular, D is a diameter of the tubular, and A is an a cross sectional area of the tubular:
and a stage resistance based at least in part on the time-domain model.
2 . The method of claim 1 , further comprising altering frac operations based at least in part on the Darcy factor of the stage resistance.
3 . The method of claim 1 , further comprising altering treatment parameters such as proppant concentration, pumping rate, or completions design, based at least in part on the Darcy factor or the stage resistance.
4 . The method of claim 1 , wherein the pressure is measured by one or more transducers disposed on a wellhead of the wellbore.
5 . The method of claim 1 , further comprising inverting the pressure.
6 . The method of claim 1 , wherein the time-domain model is a best fit model.
7 . The method of claim 1 , wherein the stage resistance is an aggregate resistance of one or more perforations in the wellbore.
8 . A non-transitory machine-readable medium having data stored therein representing a software executable by a computer, the software executable comprising instructions configured to:
recording from a transducer one or more measurements a pressure created by a tube wave in a tubular of a wellbore at a wellhead;
creating a time-domain model based at least in part on the pressure; and
identifying a Darcy factor and a stage resistance based at least in part on the time-domain model, wherein the stage resistance is found using
R
=
RA
ρ
0
V
w
,
where R is the stage resistance, R is a resistance in a tubular, A is a cross sectional area of the tubular, ρ 0 is a fluid density, and V w is a speed of the tube wave in the tubular.
9 . The non-transitory machine-readable medium of claim 8 , further comprising altering frac operations based at least in part on the Darcy factor of the stage resistance.
10 . The non-transitory machine-readable medium of claim 8 , further comprising altering treatment parameters such as proppant concentration, pumping rate, or completions design, based at least in part on the Darcy factor or the stage resistance.
11 . The non-transitory machine-readable medium of claim 8 , wherein the transducer is disposed on the wellhead of the wellbore.
12 . The non-transitory machine-readable medium of claim 8 , further comprising inverting the pressure.
13 . The non-transitory machine-readable medium of claim 8 , wherein the time-domain model is a best fit model.
14 . The non-transitory machine-readable medium of claim 8 , wherein the Darcy factor is found using
α
=
fLQ
0
2
V
w
DA
,
where the α is a pipe friction, f is a friction factor, L is a length of one or more tubulars in the wellbore, Q o is a flow rate, V w is a speed of the tube wave in the tubular, D is a diameter of the tubular, and A is an a cross sectional area of the tubular.
15 . The non-transitory machine-readable medium of claim 8 , wherein the stage resistance is an aggregate resistance of one or more perforations in the wellbore.
16 . A system comprising:
a transducer to measure a pressure created by a tube wave at a wellhead; and
an information handling system connected to the transducer and configured to:
create a time-domain model based at least in part on the pressure; and
identify a Darcy factor and a stage resistance based at least in part on the time-domain model, wherein the stage resistance is found using
R
=
RA
ρ
0
V
w
,
where R is the stage resistance, R is a resistance in the tubular, A is a cross sectional area of the tubular, ρ 0 is a fluid density, and V w is a speed of the tube wave in the tubular.
17 . The system of claim 16 , wherein the information handling system is further configured to alter a frac operation based at least in part on the Darcy factor of the stage resistance.
18 . The system of claim 16 , wherein the transducer disposed on the well head is configured to measure the pressure.
19 . The system of claim 16 , wherein the transducer disposed on the well head is configured to measure the tube wave.
20 . The system of claim 16 , wherein the information handling system is configured to alter frac operations based at least in part on the Darcy factor of the stage resistance.