Part - 1 Drill bit optimization algorithm

development

Graphical approach

07-07-2012

Ankit Kukreja at Weatherford International

Introduction

• Drilling optimization is the logical process of analyzing effects and interactions of drilling variables through mathematical modeling to achieve maximum drilling efficiency.

• The process involves the post appraisal of offset well record to determine the cost effectiveness of selected control variables, which include mud type, hydraulics, bit type, weight on bit and rotary speed.

• The variables that offer the best potential for improving the drilling process are identified.

Optimization variables

• Objective – Optimize the total nozzle flow area through bit.

• Criterion – 1) Maximum Jet Impact Force

2) Maximum Bit Hydraulic Horsepower

3) Maximum Jet Velocity

• Optimization variables – Fluid flow rate and Parasitic pressure loss.

Algorithm

• Define well geometry, bit specification, fluid properties and pump specification.

• Calculate current nozzle total flow area (TFA) and maximum flow.

• Choose two flow rates and calculate corresponding parasitic pressure losses.

• Extrapolate the loss vs flow rate curve corresponding to above two points.

• Decide correct criterion and draw optimum hydraulic path. • Find the intersecting point to get optimum flow rate and

parasitic pressure loss. • Find bit pressure loss and hence, optimum effective nozzle

total flow area corresponding to the optimum point.

Results of part - 1

Please refer to the enclosed code for explicit calculations

Criterion 1: Maximum Impact Force

1.6 1.8 2 2.2 2.4 2.6 2.8 32.2

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

4

4.2

Flow Rate (gpm)

Para

sitic

Pre

ssure

Loss(p

si)

Well dynamics (in blue) and optimum hydraulic path (in red and green)

Parasitic losses vs Flow rate (log-log plot)

Optimum point

X 1

03

Criterion 2: Maximum Bit Hydraulic Horsepower

1.6 1.8 2 2.2 2.4 2.6 2.8 32.2

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

4

4.2

Flow Rate (gpm)

Para

sitic

Pre

ssure

Loss(p

si)

Well dynamics (in blue) and optimum hydraulic path (in red and green)

Parasitic losses vs Flow rate (log-log plot)

Optimum point X 1

03

Criterion 3: Maximum Jet velocity

1.6 1.8 2 2.2 2.4 2.6 2.8 32

2.5

3

3.5

4

4.5

Flow Rate (gpm)

Para

sitic

Pre

ssure

Loss(p

si)

Well dynamics (in blue) and optimum hydraulic path (in red and green)

Parasitic losses vs Flow rate (log-log plot)

Optimum point X 1

03

Part - 2 Surge/Swab pressure calculation

algorithm development

Introduction

• The movement of the drill string when pulling out of

the hole will cause the pressure caused by the drilling fluid on the bottom of the hole to decrease.

• This caused by the friction between the movement of the pipe and the stationary drilling mud. This is referred to as swab pressure.

• The reverse is also true, running in the hole the pressure will increase due to the pipe movement, this is called surge pressure.

• The swab and surge pressure need to be control so the well does not form a kick or break down the formation.

Notations - Flow rate due to pipe movement - Pipe velocity - Pipe internal diameter - Pipe outer diameter - Casing internal diameter - Average fluid velocity - Average fluid velocity taking pipe movement into account - Constant depending on fluid - Total nozzle flow area - Fraction of flow through annulus - Flow rate through annulus - Flow rate through pipe

1

2

p

t

c

j

a

a

p

q

v

d

d

d

v

v

K

A

f

q

q

Algorithm - Closed pipe end

• Calculate flow rate due to movement of pipe

• Calculate from the above obtained flow rate.

• Now,

where Kc is decided initially depending on the fluid.

• Calculations of pressure loss and EMW is given in the code.

2

1( )

4

pv dq

v

*t c pv v K v

Algorithm - Open pipe end • Find optimum total nozzle flow area from Drill bit optimization

algorithm. • Keep,

where fa is fraction of flow through annulus. • Calculate velocity, from above flow rate. • Again, the total velocity is

• Do pressure calculations. • Run the above steps and find fa in such a way that the pressure loss

through pipe and annulus balances out. • After getting the final fa value, do pressure calculations once again

to get the pressure loss.

2

1

2

1

[ / 4* ]

(1 ) [ / 4* ]

a a p

p a p

q f v d Aj

q f v d Aj

v

*t c pv v K v

Please refer code for calculations

Thank you

- Ankit Kukreja