To study the effects of downhole problem on torque and drag calculation in directional wells

Presented by:Nikhil BarshettiwarME (Petroleum)Maharashtra Institute of Technology, Pune

Contents

• •Basics of Torque and Drag calculation

•Soft string models and Stiff string models

•Areal Clearance Factor Calculation

•Analysis of results by analytical methods

•Introduction to finite element analysis

•Contact force calculation

•Results

•Conclusion

F1

F2 = F1 + We*L + μ*Fn

Soft String Model Vs Stiff String Model

Areal Clearance Factor

0 50 100 150 200 2500

20

40

60

80

100

120

140

160

180

200

f(x) = 3.05619146579862E-05 x³ − 0.0104084190050753 x² + 1.61261808901416 xR² = 0.998775435163933

Thickness Vs Hole Angle

Logarithmic (Thickness Vs Hole Angle)

Polynomial (Thickness Vs Hole Angle)

Thickness(mm)

Cent

ral a

ngle

(deg

ree)

Central Angle Vs Thickness

0 20 40 60 80 100 120 140 160 180 2002000

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000f(x) = NaN x^NaNR² = NaNf(x) = NaN x^NaNR² = NaNf(x) = NaN x^NaNR² = NaNf(x) = 0R² = 0

Angle Vs Increase in DragPower (Angle Vs Increase in Drag)Power (Angle Vs Increase in Drag)Power (Angle Vs Increase in Drag)Power (Angle Vs Increase in Drag)Power (Angle Vs Increase in Drag)Power (Angle Vs Increase in Drag)Logarithmic (Angle Vs Increase in Drag)Power (Angle Vs Increase in Drag)Logarithmic (Angle Vs Increase in Drag)Polynomial (Angle Vs Increase in Drag)

Angle at the center (degrees)

Incr

ease

in d

rag

(lb)

Drag Vs Central Angle

0 50000 100000 150000 200000 2500000

2000

4000

6000

8000

10000

12000

Exxon Model-HoistingExxon Model-Lowering3D Analytical Model -Hoisting3D Analytical model (Lowering)

Hook load (lb)

Dep

th (f

t)

Drag (Original Case)

0 50000 100000 150000 200000 2500000

2000

4000

6000

8000

10000

12000

Exxon model (Hoisting)Exxon model-(lowering)3D Analytical Model (Hoisting)3D Analytical Model (lowering)

Hook Load (lb)

(Dep

th,ft

)

Drag (10 mm thickness)

0 50000 100000 150000 200000 250000 300000 350000 4000000

2000

4000

6000

8000

10000

12000

Exxon Model (Hoisting)Exxon model (lowering)3D Analytical model (hoisting)3D analytical (lowering)

Hook Load (lb)

Dept

h (ft

)

Drag (100 mm thickness)

0 100000 200000 300000 400000 500000 600000 700000 8000000

2000

4000

6000

8000

10000

12000

Exxon Model (hoisting)Exxon model (lowering)3D analytical model (hoisting)3D analytical model (lowering)

Hook load (lb)

Dep

th (f

t)

Drag (150 mm thickness)

Introduction to FEM

Developing MATLAB Code

Input Data, Boundary Conditions

Results

Input data for MATLAB Program

1. Drill string specifications - Length of drillpipe - Diameters - Density of Pipe - Young’s Modulus -Poisson’s ratio

2. Survey data - Measured depth - Inclination - Azimuth

3. Controlling parameters for Wilson-theta method - Time step - alpha and beta -Total steps -Clearance - Stiffness

4. Boundary Conditions

nnd=4;nel=3;nne=2;nodof=6;eldof=nne*nodof;%%nodes coordinates X and Y %%%geom=zeros(nnd,1);geom=[0.;a.;b.;c.];%%element connectivity%%%connec=zeros(nel,2);connec=[1 2;2 3;3 4];%%geometrical properties%%%%%prop(1,1)=E; prop(1,2)=Iprop=zeros(nel,2);prop=[200000 200e6;200000 200e6;200000 200e6];%%%Boundry conditions%%%nf=ones(nnd,nodof);nf(1,1)=0; nf(1,2)=0;nf(2,1)=0;nf(3,1)=0;nf(4,1)=0; nf(4,2)=0; %%counting the no. of degrees of freedom%%%n=0;for i=1:nnd for j=1:nodof if nf(i,j)~=0 n=n+1; nf(i,j)=n; end endend %%%%Internal Hinges%%%Hinge=ones(nel,2); %%loading%%%Joint_loads=zeros(nnd,2);%%%Enter here the forces in X and Y directions at node iElement_loads=zeros(nel,4);Element_loads(1,:)=[-1.e4 -1.e7 -1.e4 1.e7];Element_loads(2,:)=[-1.e4 -8.333e6 -1.e4 8.3333e4];%%%%%End of Input %%%%%%

Solution for FEA using Newmark-Beta Method

Steps involved in FEM

1. Setting up matrices [M], [K] and [C]

2. Initialize {X}, {X’} and {X”}

3. Selection of time steps Δt , calculating α and β

4. Forming effective stiffness matrix

5. Calculating effective force vector

6. Solving for Displacement matrix at t+Δt

7. Calculating Velocity and Acceleration matrix

Contact Force

05/01/2023 17REFERENCE-ANSYS Mechanical APDL Rotordynamic

Results

Depth (ft)Force (lb)

Force(lb), 10mm Force(lb),100mmForce(lb),150 mm

Hoisting Lowering Hoisting Lowering Hoisting Lowering Hoisting Lowering

5801.894 95818.86 93271.26 96648.72 94079.05 140567.7 136830.4 290027.4 282316.2

5898.293 94335.02 91994.88 95152.03 92791.62 138390.9 134957.9 285536 278452.8

5994.003 92861.82 90727.5 93666.07 91513.26 136229.7 133098.6 281076.9 274616.7

6089.32 91397.35 89454.88 92188.91 90229.63 134081.3 131231.7 276644.2 270764.7

6184.899 89929.98 88174.68 90708.83 88938.33 131928.7 129353.6 272202.7 266889.7

6280.642 88460.55 86890.7 89226.68 87643.23 129773 127470 267755 263003.3

Results50000

100000

150000

200000

250000

300000

350000

400000

5500

5600

5700

5800

5900

6000

6100

6200

6300

6400

Force (10mm-Hoisting)Force (10mm-lowering)Force (100mm-Hoisting)Force (100mm-lowering)Force (150mm-Hoisting)Force (150mm-lowering)

Force (lb)

Dept

h (ft

)

• Increase in drag linearly with increase in bed thickness

• Base case value is 2000 lb assume for calculations. Increase in drag for 10mm, 100mm and 150mm are obtained as 2017.321 lb, 2934.031 lb and 6037.383 lb respectively.

Conclusion•Analytical model gives exaggerated results since it assumes the complete drillstring is in contact with the cutting bed.

•Finite Element Analysis with help of contact analysis can improve the results because it takes stiffness of drillstring into account, hence the increase amount of drag wherever contact force is occurring.

•There is always fold increase in torque and drag due to accumulation of cuttings bed. The amount of increase in drag due to this can reduce the efficiency of equipments.

References

1.Aadnoy,S.B., Fazaehizadeh, M.,Hareland,G. “A 3D Analytical model for wellbore friction”, JCPT, vol.49,No.10, October 2010  2.Aadnoy,B.S.,Andersen,K. “Friction analysis for long reach wells” ,SPE/IADC 39391,IADC/SPE Drilling Conference held in Dallas, Texas, 3-6 March 1998 3.Fazaelizadeh, M.,Hareland,G.,Aadnoy,B.S. “Application of New 3-D Analytical Model for Directional Wellbore Friction” Modern applied science , Vol.4 No.2 February 2012 4.Fazaelizadeh,M. “Real time Torque and Drag Analysis during Directional Drilling, Ph.d Thesis, Department of chemical and Petroleum engineering, Calgary, Alberta, March 2013) 5. Francis Effiong., ‘Experimental cuttings transport in horizontal wellbore-The determination of cuttings bed height’, NTNU. 6. Haduch,G.A.,Procter,R.L., Samuels,D.A. “Solution of common stuck pipe problems through the adaption of Torque/Drag Calculations” IADC/SPE 27490,IADC/SPE Drilling Conference held in Dallas, Texas, 15-18 February 1994)  7. Hareland,G.,Wu,A.,Fazaelizadeh,M. “Finite element analysis of drillstring and Its application on torque and drag calculation, The International Journal of Engineering and Science, Vol.2,Issue 2, Pages 9-16, 2013.

8. Johancsik,C.A.,Friesen,D.B.,Dawson,R. “Torque and Drag in Directional Wells- Prediction and Measurement” ,1983 IADC/SPE Drilling Conference held in New Oriens 20-23 Feb  

10. Maidla,E.,Haci,M. “Understanding Torque: The Key to slide-drilling Directional wells”, IADC/SPE 87162, IADC/SPE drilling conference held in Dallas, Texas, USA,2-4 March 2004

11. Mirhaj, S.A., Kaarstad, E.,Aadnoy, B.S. “Improvement of Torque and Drag modeling in Long reach wells” Modern applied science, Vol.5 No.5 october 2011

12.Orkhan Ismayilov ,”Application of 3-D Analytical Model for wellbore friction calculation in actual wells”Norwegian Institute of Science and Technology, Department of Petroleum Engineering and Applied Geophysics  13.Wu, A., Hareland ,G. “Calculation of friction coefficient and downhole weight on bit with finite element analysis of drillstring”,ARMA 12-195, 46th rock mechanics/geomechanics symposium held in Chicago, IL,USA, 24-27 June 2012

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