# US 8,543,336 B2 · Distributed measurement of mud temperature

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- Number: US 8,543,336 B2
- Document ID: US8543336B2
- Status: Granted
- Kind: B2
- Application number: 12/582,742
- Filed: 2009-10-21
- Published: 2010-04-29
- Granted: 2013-09-24
- Earliest claimed: 2008-10-22
- Assignees: Baker Hughes Incorporated
- Applicants: John D. Macpherson
- Inventors: John D. Macpherson
- Web page: https://patentgrep.com/patent/US8543336B2

## CPC

- E21B 47/06: Measuring temperature or pressure
- E21B 47/07: Temperature
- G01K 1/026: {arrangements for monitoring a plurality of temperatures, e.g. by multiplexing}
- G01K 7/42: Circuits effecting compensation of thermal inertia; Circuits for predicting the stationary value of a temperature
- E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- G01K: MEASURING TEMPERATURE; MEASURING QUANTITY OF HEAT; THERMALLY-SENSITIVE ELEMENTS NOT OTHERWISE PROVIDED FOR (radiation pyrometry G01J5/00)

## Abstract

A method for estimating a temperature within sub-surface materials traversed by a wellbore includes: obtaining temperature data from a plurality of measurements of temperature taken within the wellbore; calculating an overall heat transfer coefficient from the measurement data; calculating a geothermal gradient from the overall heat transfer coefficient; and using the geothermal gradient to estimate the temperature within the sub-surface materials. A system and a computer program product are provided.

## Claims

### Claim 1

A method for estimating a far-field temperature within a formation penetrated by a borehole, the method comprising:
sensing temperatures during circulation of a drilling fluid using a plurality of temperature sensors distributed along a drill string to provide temperature measurement data;
calculating an overall heat transfer coefficient from the temperature measurement data obtained only during circulation of the drilling fluid and from a drilling fluid film heat transfer coefficient using a processor;
calculating a geothermal gradient in the formation over a depth interval from the overall heat transfer coefficient using the processor; and
using the geothermal gradient to estimate the far-field temperature within the formation using the processor.

### Claim 2 (depends on 1)

The method as in claim 1, wherein calculating the overall heat transfer coefficient comprises combining heat transfer coefficients associated with sections of the borehole.

### Claim 3 (depends on 1)

The method as in claim 1, further comprising: combining a plurality of heat transfer coefficients to provide the overall heat transfer coefficient.

### Claim 4 (depends on 3)

The method as in claim 3, wherein combining comprises performing at least one of: averaging, a linear fit, a logarithmic fit, an exponential fit, a fit to a power function, a weighted fit and a least squares fit.

### Claim 5 (depends on 1)

The method as in claim 1, wherein the temperature data comprises measurements taken at a plurality of depths within the borehole.

### Claim 6 (depends on 1)

The method as in claim 1, the temperature data comprises temperature taken at least one of internal to a drill string and external to a drill string.

### Claim 7 (depends on 1)

The method as in claim 1, further comprising estimating the overall heat transfer coefficient by estimating a thermal resistance for at least one of: drilling fluid within a drill string; drilling fluid crossing a wall of a drill string; and drilling fluid external to a drill string and within the borehole.

### Claim 8 (depends on 1)

The method as in claim 1, further comprising estimating at least one of: a temperature at a total depth of the borehole and a temperature within the formation at a given radius from a center of the borehole.

### Claim 9 (depends on 1)

The method as in claim 1, further comprising accounting for at least one operational factor in the calculating of a geothermal gradient.

### Claim 10

A system for determining a far-field temperature within a formation penetrated by a borehole, the system comprising:
a plurality of temperature sensors distributed along a drill string, the drill string providing for the borehole that penetrates the formation; and
a processor for receiving temperature data sensed during circulation of a drilling fluid from the plurality of temperature sensors along at least a portion of the borehole and for implementing machine executable instructions for calculating an overall heat transfer coefficient from the measurement data obtained only during circulation of the drilling fluid and from a drilling fluid film heat transfer coefficient; calculating a geothermal gradient in the formation over a depth interval from the overall heat transfer coefficient; and using the geothermal gradient to estimate the far-field temperature within the formation.

### Claim 11 (depends on 10)

The system as in claim 10, wherein the processor is equipped to implement the machine executable instructions in real time.

### Claim 12 (depends on 10)

The system as in claim 10, further comprising an input for receiving at least one parameter of operational data.

### Claim 13 (depends on 12)

The system as in claim 12, wherein the processor further comprises instructions for using the operational data to estimate the temperature within the formation.

### Claim 14 (depends on 10)

The system as in claim 10, wherein the parameter of operational data comprises at least one of radius, flow rate, revolutions per minute and volume.

### Claim 15 (depends on 10)

The system as in claim 10, wherein the plurality of temperature sensors is distributed at least one of internally and externally along the drill string.

### Claim 16

A non-transitory computer readable medium comprising computer executable instructions for estimating a far-field temperature in a formation penetrated by a borehole, that when executed by a computer, cause the computer to perform the steps of:
receiving temperature data sensed during circulation of a drilling fluid from a plurality of measurements of temperature taken by a plurality of temperature sensors distributed along a drill string within the borehole traversed by a logging instrument;
calculating an overall heat transfer coefficient from the measurement data obtained only during circulation of the drilling fluid and from a drilling fluid film heat transfer coefficient;
calculating a geothermal gradient in the formation over a depth interval from the overall heat transfer coefficient;
using the geothermal gradient to estimate the temperature in the formation; and
outputting the estimate to a user.

### Claim 17 (depends on 16)

The non-transitory computer readable medium as in claim 16, further comprising the step of receiving an input for a selected depth within the formation and estimating the temperature in the formation at the selected depth.

### Claim 18 (depends on 1)

The method as in claim 1, wherein using the geothermal gradient comprises multiplying a depth times the geothermal gradient and adding the product to a surface temperature to estimate the far-field temperature within the formation at the depth.

### Claim 19 (depends on 1)

The method as in claim 1, wherein calculating the geothermal gradient comprises solving an equation comprising a flowline temperature, a depth, a temperature in an annulus at the depth, and a mud inlet temperature.

### Claim 20 (depends on 19)

The method as in claim 19, wherein the equation further comprises a surface temperature.

### Claim 21 (depends on 1)

The method as in claim 1, wherein calculating the overall heat transfer coefficient comprises solving an equation comprising a radius to a point on the formation and a thermal conductivity of the formation.

### Claim 22 (depends on 1)

The method as in claim 1, wherein the drilling fluid film heat transfer coefficient comprises at least one of a film coefficient for an inside wall of the drill string, a film coefficient for an outside wall of the drill string, and a film coefficient for a borehole wall.

### Claim 23 (depends on 22)

The method as in claim 22, further comprising estimating the film coefficient for an outside wall of the drill string using drill string rotary speed as an input.