# US 7,412,331 B2 · Method for predicting rate of penetration using bit-specific coefficient of sliding friction and mechanical efficiency as a function of confined compressive strength

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- Number: US 7,412,331 B2
- Document ID: US7412331B2
- Status: Granted
- Kind: B2
- Application number: 11/015,899
- Filed: 2004-12-16
- Published: 2006-07-06
- Granted: 2008-08-12
- Earliest claimed: 2004-12-16
- Assignees: Chevron U.S.A. Inc.
- Inventors: William Malcolm Calhoun; Hector Ulpiano Caicedo; Russell Thomas Ewy
- Web page: https://patentgrep.com/patent/US7412331B2

## CPC

- E21B 44/00: Automatic control systems specially adapted for drilling operations, i.e. self-operating systems which function to carry out or modify a drilling operation without intervention of a human operator, e.g. computer-controlled drilling systems; Systems specially adapted for monitoring a plurality of drilling variables or conditions
- E21B 45/00: Measuring the drilling time or rate of penetration
- E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS

## Abstract

A method for predicting the rate of penetration (ROP) of a drill bit drilling a well bore through intervals of rock of a subterranean formation is provided. The method uses an equation based upon specific energy principles. A relationship is determined between a bit-specific coefficient of sliding friction μ and confined compressive strength CCS over a range of confined compressive strengths CCS. Similarly, another relationship for the drill bit is determined between mechanical efficiency EFFM and confined compressive strength CCS over a range of confined compressive strengths CCS. Confined compressive strength CCS is estimated for intervals of rock through which the drill bit is to be used to drill a well bore. The rate of penetration ROP is then calculated utilizing the estimates of confined compressive strength CCS of the intervals of rock to be drilled and those determined relationships between the bit-specific coefficient of sliding friction μ and the mechanical efficiency EFFM and the confined compressive strengths CCS, as well as using estimated drill bit speeds N (RPM) and weights on bit (WOB).

## Claims

### Claim 1

A method for predicting the rate of drilling of a well bore in a subterranean formation, the method comprising the steps of:
A) determining the rate of penetration (ROP) of a drill bit drilling a well bore through intervals of rock of a subterranean formation by:
a) determining for at least one type of drill bit a relationship between a bit-specific coefficient of sliding friction μ and confined compressive strength CCS over a range of confined compressive strengths CCS;
b) determining for the at least one type of drill bit a relationship between mechanical efficiency EFFM and confined compressive strength CCS over a range of confined compressive strengths CCS;
c) determining the confined compressive strength for intervals of rock through which the at least one type of drill bit is to be drilled to form a well bore; and
d) calculating the rate of penetration ROP for the at least one type of drill bit drilling along the intervals of rock to create a well bore, the calculations utilizing the confined compressive strength of the intervals of rock being drilled and the relationships between the bit-specific coefficient of sliding friction μ and the mechanical efficiency EFFM and the confined compressive strengths CCS; and
B) selecting a drill bit for drilling the well bore through the intervals of rock of the subterranean formation based on the calculated rate of penetration ROP;
wherein the confined compressive strength (CCS) of an interval of rock is determined at least in part based upon the unconfined compressive strength (UCS) of the interval of rock, the equivalent circulating density (ECD) of a drilling fluid being used to drill the interval of rock, the overburden stress (OB) removed from the interval of rock being drilled, the in situ pore pressure (PP) of pore fluids proximate the interval of rock being drilled, and the permeability of the interval of rock being drilled.

### Claim 2 (depends on 1)

The method of claim 1 wherein:
the relationship between the bit-specific coefficient of sliding friction μ and the confined compressive strength CCS over a range of confined compressive strengths CCS for the at least one type of drill bit is dependent upon the weight of the drilling fluid being used to drill an interval of rock.

### Claim 3 (depends on 1)

The method of claim 1 wherein:
the relationship between the bit-specific coefficient of sliding friction μ and the confined compressive strength CCS over a range of confined compressive strengths CCS is dependent upon the size of the cutters for polycrystalline diamond compound (PDC) bits.

### Claim 4 (depends on 1)

The method of claim 1 wherein:
the relationship between the mechanical efficiency EFFM and the confined compressive strength CCS over a range of confined compressive strengths CCS for at least one drill bit is dependent upon the weight of the drilling fluid being used to drill the well bore.

### Claim 5 (depends on 1)

The method of claim 1 further comprising:
determining a relationship, for the at least one type of drill bit, between the revolutions per minute (N) at which the at least one type of drill bit is to be operated and confined compressive strength CCS over a range of confined compressive strengths CCS; and
calculating the rate of penetration ROP for the at least one type of drill bit drilling through the intervals of rock to create a well bore utilizing the confined compressive strength of the intervals of rock being drilled and the relationships between the bit-specific coefficient of sliding friction u, the mechanical efficiency EffM and the revolutions per minute (N) at which the drill bit is to be operated and the confined compressive strengths.

### Claim 6 (depends on 1)

The method of claim 1 further comprising:
determining a relationship for the at least one drill bit between the weight on bit (WOB) at which the at least one drill bit is to be operated and confined compressive strength CCS over a range of confined compressive strengths CCS; and
calculating the rate of penetration for the at least one type of drill bit drilling along the intervals of rock utilizing the confined compressive strength of the intervals of rock being drilled and the relationships between the bit-specific coefficient of sliding friction u, the mechanical efficiency EffM, and WOB at which the bit should be operated and confined compressive strength.

### Claim 7 (depends on 1)

The method of claim 1 wherein:
the rate of penetration is calculated in accordance with the following mathematical expression:
ROP
=
13.33
⁢
⁢
μ
⁢
⁢
N
D
B
⁡
(
CCS
EFF
M
·
WOB
-
1
A
B
)
where: ROP=Rate of penetration (ft/hr);
μ=bit-specific coefficient of sliding friction;
N=revolutions per minute of the at least one drill bit;
CCS=Confined compressive strength (psi) of the rock in the interval being drilled;
WOB=weight on bit (lbs);
EFFM=Mechanical efficiency (%);
DB=Bit diameter (in); and
AB=Borehole area (sq-in) of the well bore being drilled.

### Claim 8 (depends on 1)

The method of claim 1 wherein:
CCS is calculated in accordance with the following mathematical expression for intervals of rock having low permeability:
CCS=UCS+f(DP)
where UCS=Unconfined Compressive Strength for the rock; and;
f(DP)=function of the differential pressure DP applied across the rock during drilling.

### Claim 9 (depends on 1)

The method of claim 1 wherein:
CCS is calculated in accordance with the following mathematical expression for intervals of rock having low permeability:
CCSLP=UCS+DPLP+2DPLP sinFA/(1−sinFA);
where: DPLP=ECD pressure−(PP−(OB-ECD)/3);
ECD=Equivalent Circulating pressure;
PP=in situ Pore Pressure; and
OB=Overburden pressure.

### Claim 10 (depends on 9)

The method of claim 9 wherein:
CCS is calculated in accordance with the following mathematical expression for intervals of rock having high permeability:
CCS=UCS+DP+2DP sinFA/(1−sinFA)
where: UCS=Unconfined Compressive Strength of the rock;
DP=ECD−PP;
DP=differential pressure between bottom hole pressure exerted by ECD and in-situ pore pressure; and
FA=the internal angle of friction of the rock.

### Claim 11 (depends on 1)

The method of claim 1 wherein:
the step of determining relationships between the coefficient of sliding friction μ and the mechanical efficiency EffM of at least one drill bit as a varying function of a range of confined compressive strengths is bit wear dependent.

### Claim 12

A method for predicting the rate of drilling of a well bore in a subterranean formation, the method comprising the steps:
A) back calculating confined compressive strength CCS of rock in an interval of a subterranean formation in which a well bore has been drilled using a type of drill bit and drilling fluids by:
a) measuring (i) the rate of penetration (ROP); (ii) weight on bit (WOB); (iii) bit torque T; and (iv) the revolutions per minute (N) used during the drilling through an interval of rock in a subterranean formation by the type of drill bit;
b) estimating the coefficient of sliding friction μ during the drilling through the interval of rock; and
c) selecting a value of CCS from a predetermined relationship between μ and CCS for the type of drill bit; and
B) selecting a drill bit for further drilling of a well bore in an interval of rock of the subterranean formation based on the selected value of CCS; and
C) back calculating the unconfined compressive strength UCS of the rock in the interval in accordance with the following mathematical expression:
CCS=UCS+DP+2DP sinFA/(1−sinFA)
where: UCS=rock unconfined compressive strength;
DP=differential pressure (or confining stress) across the rock; and
FA=internal angle of friction of the rock.

### Claim 13 (depends on 12)

The method of claim 12 wherein:
estimating the coefficient of sliding friction μ is calculated in accordance with the following mathematical expression:
μ
=
36
⁢
T
D
B
*
WOB
where: T=bit torque (ft-lbf);
DB=bit size (inches);
μ=bit-specific coefficient of sliding friction (dimensionless); and
WOB=weight on bit (lbs).

### Claim 14 (depends on 12)

The method of claim 12 further comprising:
determining the mechanical efficiency EFFM of the drill bit utilizing a predetermined relationship between EFFM and CCS.

### Claim 15 (depends on 12)

The method of claim 12 wherein:
mechanical efficiency EFFM is calculated in accordance with the mathematical equation:
ROP
=
13.33
⁢
⁢
μ
⁢
⁢
N
D
B
⁡
(
CCS
EFF
M
·
WOB
-
1
A
B
)
where: ROP=Rate of penetration (ft/hr);
μ=bit-specific coefficient of sliding friction;
N=revolutions per minute of the at least one drill bit;
CCS=Confined compressive strength (psi) of the rock in the interval being drilled;
WOB=weight on bit (lbs);
EFFM=Mechanical efficiency (%);
DB=Bit diameter (in); and
AB=Borehole area (sq-in) of the well bore being drilled.