This document provides an overview of geomechanical modeling and wellbore stability analysis. It discusses the need for geomechanical models to incorporate in-situ stress data, pore pressure, rock properties, and geology. The key aspects of developing a geomechanical model are outlined, including the variation of effective hoop stress around wellbores. Different failure criteria for compressional and tensile failures are presented. Methods for estimating pore pressure from logs using normal compaction trends and for determining fracture pressure from correlations with overburden stress are summarized. The sensitivity of results to pore pressure is highlighted. Top-down and bottom-up approaches to casing design based on pore pressure and fracture pressure are contrasted.

1. GEOMECHANICAL STUDY
OF
WELLBORE STABILITY
-VIDIT MOHAN

2. TOPICS
• Geomechanical Model
• Need of Geomechanical Model
• Wellbore Stability
• Developing Comprehensive Geomechanical Model
• Variation of Effective Hoop Stress
• Compressional and Tensile Failure
• Failure Criteria
• Normal Compaction Trend (NCT)
• Pore Pressure (PP) Estimation
• Observations
• Fracture Pressure (FP) Determination
• Sensitivity Analysis
• Conclusions
• References

3. • In-situ stress orientations
• In-situ stress magnitudes
• Pore Pressure
• Rock strength and mechanical
properties
• Fracture patterns
• Geology and structure
GEOMECHANICAL MODEL
Model involving detailed knowledge of:

4. NEED OF GEOMECHANICAL MODEL
Courtesy: Baker Hughes

5. ADVANTAGES OF GEOMECHANICS
Reduction of drilling problems:
• Wellbore stability analysis- Reducing stuck pipe, sidetracks, washing and reaming
• Improved pore and fracture pressure prediction- Reducing kicks and lost circulation
Improving reservoir performance:
• Predicting sand production
• Predicting permeable natural fractures to optimize production
• Prediction of fault controlled hydrocarbon column heights
• Injection or depletion induced fault reactivation
• Determination of fracture propagation direction and reorientation
• Sweep efficiency
• Compaction and subsidence

6. WELLBORE STABILITY
• Modeling anisotropic breakouts with given in-situ stress state.
• Tendency for Breakout Initiation for different stress regimes.
• Design for variations in strength.
Key is to control the width of failure zones

7. DEVELOPING COMPREHENSIVE
GEOMECHANICAL MODEL
Parameter Data
Vertical Stress, Sv(z) g‫׬‬0
𝑧
ƿ(z) dz
Minimum Horizontal Stress, Shmin
XLOT, LOT, minifrac, lost circulation,
ballooning
Maximum Horizontal Stress, SHmax Analysis of wellbore failure
Pore Pressure, Pp
Measurements (RFT, DST, etc), Log-
based, Seismic
Stress orientation Orientation of wellbore failures
Faults/Bedding Planes Wellbore Imaging
Rock Strength
Lab measurements, Logs, Modelling
wellbore failures

8. IN-SITU PRINCIPAL STRESSES
Fig.: (A) Rock formation in-situ stresses, (B) Rock formation in-situ principal
stresses for a drilled vertical well
A B

9. VARIATION OF EFFECTIVE HOOP
STRESS
SHmax = 90 MPa
SHmax orientation is N90E (East West)
Sv= 88.2 MPa
Shmin= 51.5 MPa
Pp=Pmud=31.5 MPa

10. COMPRESSIONAL AND TENSILE
WELLBORE FAILURES

11. MOHR-COULOMB FAILURE CRITERION
Represents linear envelope obtained from plot of shear strength of material versus applied
normal stress,
τ = Б tan(Ø) + c
where τ is the shear strength, Б is the normal stress, c is the intercept of failure envelope
with the τ axis, and Ø is the slope of failure envelope.

12. VON MISES FAILURE CRITERION
• Yielding of materials begins when second deviatoric stress invariant reaches
yield strength.
• Mathematically, the von Mises yield criterion is expressed as:
J2
0.5 = (1/30.5)*( б1- б3)
Бm- Po= {( б1+ 2*б3) – Po}/3
Бv= бy= (3*J2)0.5
БV
2= 3*J2=3*k2
Бv
2 = [ (Б11- Б22)2 + (Б22- Б33)2 + (Б33- Б11)2 + 6*(Б23
2+ Б31
2+ Б12
2)]/2

13. NORMAL COMPACTION TREND (NCT)
• Straight line in log linear space fitted as a function of depth where sediments are
compacting.
• Response of petrophysical properties to reduction of porosity due to compaction
disequilibrium.
• Basis for measuring pressure from seismic, from wireline and in basin modelling.

14. PLOTTING NCT
Estimate the onset of overpressure
1.
• Plot porosity vs. depth.
2.
• Estimate porosity assuming an exponential compaction trend.
• Ø = Øo * e^ (-c*h), where ϕ is the porosity, ϕ0 is the initial porosity & c is the
coefficient of compaction
3.
• Calculate the theoretical compaction trend. Db=Dma*(1-Ø) + Dfl*Ø
• Plot this trend on the same plot as the porosity data.

15. Db=Dma*(1-Ø) + Dfl*Ø and Ø = Øo * e-c*h
Bulk Density = Db
Density of Fluid = Dfl
Density of Matrix = Dma
h=Depth
Onset of Overpressure

16. PLOTTING NCT
Using Sonic Transit Time data
ΔTn=ΔTm+ (ΔTml-ΔTm) exp (-cz)
where,
ΔTml=Mudline Transit Time
ΔTm=Compressional Transit Time
z=Depth
c=0.27 (Sandstone)
Onset of Overpressure

17. PORE PRESSURE ESTIMATION

18. EQUIVALENT DEPTH METHOD
NCT is fitted to the decrease in slowness as a
function of depth where sediments are normally
compacting.
The effective stress at depth Z is equal to
effective stress at depth A, and thus, the pore
pressure at depth Z is
Pz = Pa + (Sz–Sa).
where Pa,z and Sa,z are pore pressure and stress
at z, the depth of interest and a, the depth along
the normal compaction trend at which the
measured parameter is the same as it is at the
depth of interest.

19. RATIO METHOD
Pore pressure is the product of the normal pressure multiplied (or divided by)
the ratio of the measured value to the normal value for the same depth.
where the subscripts n and log refer to the normal and measured
values of density, resistivity, or sonic delta-t; Pp is the actual pore
pressure, and Phyd is the normal hydrostatic pore pressure.
Can lead to unphysical situations, such as calculated pore pressures that are
higher than the overburden.
Pp=Phyd ΔTlog/ΔTn

20. EATON METHOD
PP=S-[(S-Ph)*(ΔTlog/ΔTn)3]
S=Overburden Stress
Ph=Hydrostatic Pore Pressure
If the NCT is defined over an interval with elevated pore pressure, the method
will give the wrong (too low) pore pressure, leading to severe risks for drilling.

22. OBSERVATIONS
• Selection of appropriate normal compaction curve.
• Equivalent effective stress method should be used if most of overpressure is generated
by disequilibrium compaction.
• All these methods require that rock obeys a single, monotonic, compaction-induced
trend, and that no other effects are operating.
• Pore fluid properties can also have a significant effect on pore-pressure predictions.
• Fluid salinity consideration.

23. FRACTURE PRESSURE
DETERMINATION

24. FRACTURE FORMATION PRESSURE
 Fracture pressure is the pressure in the wellbore at which a formation will crack .
 Formation will fracture when pressure in borehole exceeds the least of stresses within the
rock structure.
 Normally, fractures will propagate in a direction perpendicular to the least principal
stress.
Definition and Mechanism

25. • The minimum wellbore pressure required to extend an existing fracture was
given as the pressure needed to overcome the minimum principle stress :
•The minimum principle stress in the shallow sediments is approximately one-
third the matrix stress resulting from weight of the overburden.
•Assumed elastic behaviour.
Prediction of Fracture Pressure
Hubbert and Willis Equation
fff PP  min

26. Prediction of Fracture Pressure
f
ma
ff PP 
3

f
fob
ff P
P
P 


3

3
2 fob
ff
P
P



Hubbert and Willis Equation
Pf =Pore Pressure
σob=Overburden Pressure

27. Prediction of Fracture Pressure
 Replaced the assumption that the minimum stress was one-third the matrix stress
by
where the stress coefficient was determined empirically from field data taken in
normally pressured formations.
Not valid for deeper formation.
Matthew and Kelley Correlation
maF  min

28. Prediction of Fracture Pressure
The vertical matrix stress at normal pressure is calculated (subscript “n” is for normal
pressure)
(Sma)n = Sobn – Pfn
Di is the equivalent normal pressure depth
Matthew and Kelley Correlation
iiinma DDD 535.0465.01)( 
At the depth at which the abnormal pressure presents:
535.0535.0535.0
)( ffobnma
i
PDP
D





Pfi = Fracture Initiation Pressure
Pfi= Smin + Pp
Pfi= [ (0.61*Di) - (0.61*Pp)] + Pp

29. The overburden and Poison ratio vary with depth.
Prediction of Fracture Pressure
FG=[(S-P)*ϒ/D*(1-ϒ)]+ P/D
S=Overburden
D=Depth
ϒ=Poisson Ratio
Eaton Correlation

30. Prediction of Fracture Pressure
•Stress coefficient is correlated to the bulk density of the sediments.
•Take into consideration the effect of water depth on overburden stress.
Christman Correlation
ϴ=ϴoexp(-KD)
ϴ=Porosity
K=Christman Constant
Pff= (бmin+Pp)/D
D=Depth

32. SENSITIVITY ANALYSIS
• All the methods take into consideration the pore pressure gradient.
• As the pore pressure increases, so does the fracture gradient.
• Hubbert and Willis apparently consider only the variation in pore pressure
gradient.
• Matthews and Kelly also consider the changes in rock matrix stress coefficient
and the matrix stress.
• Eaton considers variation in pore pressure gradient, overburden stress, and
Poisson’s ratio. It is probably the most accurate of the three.
• None consider the effect of water depth except Christman approach.

33. Top Down Casing Design
Pore Pressure
Fracture Pressure

34. Bottom Up Casing Design
Pore Pressure
Fracture Pressure

35. Top Down
Casing Design

36. Bottom Up
Casing Design

37. CONCLUSIONS
• Uncertainty in pore pressure prediction analyzed by examining spread in predicted
pore pressure obtained using parameter combinations consistent with available well
data.
• Pore pressure prediction from well logs has spatial and depth limitation.
• Results of wellbore stability assessment are required to mitigate consequences of
instability.
• Individual evaluation of each well.
• Pore pressure & Fracture gradient determination Casing setting depth selection

38. REFERENCES
• Drill Works – Halliburton User Guide
• Dr Mark D Zoback – Reservoir Geomechanics tutorials
• Petrophysics by Dr Paul Glover
• Well Engineering & Construction by Hussain Rabia
• European Association of Geoscientists & Engineers (EAGE) journals & short courses
• Bowers, G. L., 1995, Pore pressure estimation from velocity data: Accounting for overpressure
mechanisms besides undercompaction: SPE Drilling and Completion, 27488.
• Eaton, B. A., The equation for geopressure prediction from well logs: SPE, 5544.
• Rancom, R.C., A Method for Calculation Pore Pressures from Well Logs
• Papers:
http://petrowiki.org/Methods_to_determine_pore_pressure
http://petrowiki.org/Subsurface_stress_and_pore_pressure#Pore_pressure
 https://www.linkedin.com/groups/What-is-Normal-Compaction-Trend
3858625.S.126429683

39. THANK YOU!