1. Part - 1
Drill bit optimization algorithm
development
Graphical approach
07-07-2012
Ankit Kukreja at Weatherford International

2. 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.

3. 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.

4. 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.

5. Results of part - 1
Please refer to the enclosed code for
explicit calculations

6. Criterion 1: Maximum Impact Force
1.6 1.8 2 2.2 2.4 2.6 2.8 3
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3.8
4
4.2
Flow Rate (gpm)
ParasiticPressureLoss(psi)
Well dynamics (in blue) and optimum hydraulic path (in red and green)
Parasitic losses vs Flow rate (log-log plot)
Optimum point
X103

7. Criterion 2: Maximum Bit Hydraulic
Horsepower
1.6 1.8 2 2.2 2.4 2.6 2.8 3
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3.8
4
4.2
Flow Rate (gpm)
ParasiticPressureLoss(psi)
Well dynamics (in blue) and optimum hydraulic path (in red and green)
Parasitic losses vs Flow rate (log-log plot)
Optimum point
X103

8. Criterion 3: Maximum Jet velocity
1.6 1.8 2 2.2 2.4 2.6 2.8 3
2
2.5
3
3.5
4
4.5
Flow Rate (gpm)
ParasiticPressureLoss(psi)
Well dynamics (in blue) and optimum hydraulic path (in red and green)
Parasitic losses vs Flow rate (log-log plot)
Optimum point
X103

9. Part - 2
Surge/Swab pressure calculation
algorithm development

10. 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.

11. 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

12. 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 d
q


v
*t c pv v K v 

13. 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 

14. Please refer code for calculations
Thank you
- Ankit Kukreja