# US 8,783,355 B2 · Virtual flowmeter for a well

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- Number: US 8,783,355 B2
- Document ID: US8783355B2
- Status: Granted
- Kind: B2
- Application number: 12/967,605
- Filed: 2010-12-14
- Published: 2011-09-22
- Granted: 2014-07-22
- Earliest claimed: 2010-02-22
- Assignees: Schlumberger Technology Corporation
- Applicants: John R. Lovell; Valery Shako
- Inventors: John R. Lovell; Valery Shako
- Web page: https://patentgrep.com/patent/US8783355B2

## CPC

- E21B 47/07: Temperature
- E21B 47/103: using thermal measurements
- G01F 1/68: by using thermal effects
- G01F 1/6884: {making use of temperature dependence of optical properties}
- E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- G01F: MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME

## Abstract

A technique includes inducing a distributed temperature change along a portion of a wellbore and measuring a time varying temperature along the portion of the wellbore due to the induced change. The technique includes determining a distributed flow rate in the portion based at least in part on the measured time varying temperature before the temperature reaches equilibrium.

## Claims

### Claim 1

A method comprising:
controlling a flow device through which production fluid flows to induce a distributed temperature change along a portion of a wellbore;
measuring a time varying temperature along the portion of the wellbore due to the inducing; and
determining a distributed flow rate in the portion based at least in part on the measured time varying temperature before the temperature reaches equilibrium.

### Claim 2 (depends on 1)

The method of claim 1, wherein the measuring comprises receiving data from an array of sensors provided along the portion of the wellbore.

### Claim 3 (depends on 1)

The method of claim 1, wherein the measuring comprises receiving data from a distributed temperature sensor disposed along the portion of the wellbore.

### Claim 4 (depends on 1)

The method of claim 1, wherein the determining comprises modeling the temperature as an exponential function characterized by a time constant, determining the time constant and determining the flow rate based at least in part on the time constant.

### Claim 5 (depends on 4)

The method of claim 4, further comprising applying a linear approximation to determine a relationship between the time constant and the distributed flow rate.

### Claim 6 (depends on 1)

The method of claim 1, wherein the act of determining the distributed flow rate comprises:
determining time constants of the temperature; and
determining heat transfer coefficients based at least in part on the determined time constants.

### Claim 7 (depends on 6)

The method of claim 6, wherein the act of determining the distributed flow rate further comprises: determining a Nusselt number for a ratio of convective to conductive heat loss based at least in part on the determined heat transfer coefficients.

### Claim 8 (depends on 7)

The method of claim 7, further comprising: determining a Reynold's number based at least in part on the Nusselt number.

### Claim 9 (depends on 8)

The method of claim 8, wherein the act of determining the distributed flow rate further comprises: determining a mass flow rate based at least in part on the Reynold's number.

### Claim 10 (depends on 1)

The method of claim 1, wherein the act of determining the distributed flow rate comprises: determining a Nusselt number for a ratio of convective to conductive heat loss.

### Claim 11 (depends on 1)

The method of claim 1, wherein the act of determining the distributed flow rate comprises determining a Reynold's number.

### Claim 12 (depends on 1)

The method of claim 1, wherein a flow associated with the distributed flow comprises a turbulent flow.

### Claim 13 (depends on 1)

The method of claim 1, wherein a flow associated with the distributed flow rate is present in a production tubing, another flow is present in an annulus exterior to the production tubing, and the act of determining the distributed flow rate is based at least in part on the flow in the production tubing and the flow in the annulus.

### Claim 14 (depends on 1)

The method of claim 1, wherein a flow associated with the distributed flow rate has a time varying pressure drop induced by a time varying flow rate.

### Claim 15 (depends on 14)

The method of claim 14, wherein the pressure drop induces a change in temperature in the well due to an iso-enthalpic process.

### Claim 16 (depends on 1)

The method of claim 1, wherein the act of determining the distributed flow rate is performed at intervals of time of hydrocarbon production and the act of determining the distributed flow rate is based at least in part on a reservoir model, the method further comprising: refining the reservoir model based at least in part on a determination of the flow rate at the intervals.

### Claim 17

A method comprising:
changing a wellhead pressure to induce a distributed temperature along a portion of a wellbore;
measuring a time varying temperature along the portion of the wellbore due to the inducing; and
determining a distributed flow rate in the portion based at least in part on the measured time varying temperature before the temperature reaches equilibrium.

### Claim 18

A system comprising:
a pressure-changing device through which production fluid flows, wherein the pressure-changing device is configured to induce a temperature change;
a distributed temperature sensing system to measure a distributed temperature along at least a portion of a wellbore; and
a processing system configured to:
receive data from the distributed temperature sensor indicative of a time varying temperature along the portion of the wellbore due to the induced distributed temperature change;
determine a distributed flow rate in the portion based at least in part on the time varying temperature before the time varying temperature has reached equilibrium;
model the temperature as an exponential function characterized by at least one time constant;
determine the time constant; and
determine the distributed flow rate based at least in part on the determined time constant.

### Claim 19 (depends on 18)

The system of claim 18, wherein the pressure changing device comprises at least one of a wellhead-disposed valve or a downhole flow device.

### Claim 20 (depends on 18)

The system of claim 18, wherein the processing system is adapted to:
determine time constants of the temperature; and
determine heat transfer coefficients based at least in part on the determined time constants.

### Claim 21 (depends on 20)

The system of claim 20, wherein the processing system is adapted to:
determine a Nusselt number for a ratio of convective to conductive heat loss based at least in part on the determined heat transfer coefficients.

### Claim 22 (depends on 21)

The system of claim 21, wherein the processing system is adapted to:
determine a Reynold's number based at least in part on the Nusselt number.

### Claim 23 (depends on 22)

The system of claim 22, wherein the processing system is adapted to:
determine a mass flow rate based at least in part on the Reynold's number.

### Claim 24 (depends on 18)

The system of claim 18, wherein the processing system is adapted to:
determine a Nusselt number for a ratio of convective to conductive heat loss.

### Claim 25 (depends on 18)

The system of claim 18, wherein the processing system is adapted to:
determine a mass flow rate based at least in part on the Reynold's number.