TP00-09 1

Advanced Wellbore Stability Model

(WELLSTAB-PLUS)

Dr. William C. Maurer

TP00-09 2

DEA-139 Phase I

DEA Sponsor: MarathonDuration: 2 YearsStart Date: May 1, 2000End Date: April 30, 2002Participation Fee: $25,000/$35,000

TP00-09 3

Typical Occurrences of WellboreInstability in Shales

soft, swelling shale

brittle-plastic shale

brittle shale

naturally fractured shale

strong rock unit

TP00-09 5

Wellbore Stability Problems

High Torque and Drag

Bridging and Fill

Stuck Pipe

Directional Control Problem

Slow Penetration Rates

High Mud Costs

Cementing Failures and High Cost

Difficulty in Running and Interpreting Logs

TP00-09 7

Effect of Borehole Pressures

TP00-09 8

PW PW

smax smax

smin smin

High Support Pressure Low Support Pressure

Effect of Mud Support Pressureon Rock Yielding

TP00-09 9

Rock Failure

TP00-09 10

Rock Failure Mechanisms

PLASTICBRITTLE

TP00-09 11

Rock Yielding around WellboresLaboratory Tests

Rawlings et al, 1993

Isotropic Stresses Anisotropic Stresses

TP00-09 12

Change In Near-Wellbore StressesCaused by Drilling

sV (overburden)

sHmin

sHmax sHmin

sHmax

Pw (hydrostatic)

Before DrillingIn-situ stress state

After DrillingLower stress within wellbore

TP00-09 13

Stress Concentration around an Open Wellbore

Pw

Po

sHmin

sHmax

szsq

sq

sr

sz

sr

s

r

TP00-09 14

Strength vs StressIdentifying the Onset of Rock Yielding

Shear

Str

ess

sr´

Effective Compressive Stress

Stable Stress State

sq´

sr´

Shear

Str

ess

sr´

Effective Compressive Stress

Unstable Stress State

sq´

sr´

sq´

MinStress

MaxStress

sq´

TP00-09 15

Effect of Pore Fluid Saturation

POROUS ROCKSOLID ROCK

Pf = Fluid Pressure

so=szso=sz+pf

TP00-09 16

Effective Stresses Partioningof Total Stress between

Mineral Grains and Pore Fluids

Po s

s

s´ = s - a Pos´ - effective stress

s - total stressPo - pore pressure

a - Biot Coefficient

( 1 for weak, porous rocks)

TP00-09 17

Effective Rock Stress

sz= s o - pf

so = Overburden Stress

sz = Matrix Stress

pf = Pore Fluid Pressure

TP00-09 18

Effect of Near-WellborePore Pressure Changeon Effective Stresses

Sh

ear

Str

ess

No Yield

Yield

Effective Compressive Stress

sr´ sq´sr´ sq´

Po increase

TP00-09 19

TP00-09 20

MEI Wellbore Stability Model:(mechanical model, does not include chemical effects)

Linear elastic model (BP)

Linear elastic model (Halliburton)

Elastoplastic Model (Exxon)

Pressure Dependent Young’s Modulus Model(Elf)

TP00-09 21

Mathematical Algorithms

Dr Martin Chenervert (Un. Texas)

Dr. Fersheed Mody (Baroid)

Jay Simpson (OGS)

Dr. Manohar Lal (Amoco)

Dr. Ching Yew (Un. Texas)

TP00-09 22

Stress State on Deviated Wellbore

s3

s2sz sr

tqzbq

tzq

sq

a

s1

TP00-09 23

TP00-09 24

(BP)Linear Elastic Model

TP00-09 25

TP00-09 26

(Halliburton)Linear Elastic Model

TP00-09 27

TP00-09 28

(Exxon)Elastoplastic Model

TP00-09 30

TP00-09 31

TP00-09 33

(Elf)Pressure Dependent

Young’s Modulus

TP00-09 34

TP00-09 35

Shale Borehole Stability TestsDarley, 1969

DIESELDISTILLED WATER

TP00-09 36

Montmorillonite Swelling PressurePowers, 1967

80,000

60,000

40,000

20,000

04th 3rd 2nd 1st

5000

4000

3000

2000

1000

0

SW

ELLIN

G P

RESSU

RE, psi

kg/c

m2

LAYERS OF CRYSTALLINE WATER

TP00-09 37

Shale Water AdsorptionChenevert, 1970

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

5

4

3

2

1

0

WEIG

HT %

WATER

WATER ACTIVITY - aW

DESORPTION

ADSORPTION

TP00-09 38

Shale Swelling TestsChenevert, 1970

TIME - HOURS

LIN

EAR S

WELLIN

G -

%

.01 0.1 1.0 10

0.4

0.3

0.2

0.1

0

-0.1

1.00

0.910.880.840.75

0.25

Activity of Internal Phase

TP00-09 39

Effect of K+Ions on Shale SwellingBaroid, 1975

Ca ++

K+

K+

K+

Na+

Cs+

Na+

Ca++

Li+

K+

Rb+

Cs+

Na+

Mg++

Na+

10A°

Na+

--

--

-

--

-

-

-

-- -

-

-

TP00-09 41

North Sea Speeton Shale SpecimenExposed at Zero DP to Drilling Fluid

Drilling Fluid:

Ionic Water-Base

(CaCl2 Brine)

Activity = 0.78

TP00-09 42

North Sea Speeton Shale SpecimenExposed at Zero DP to Drilling Fluid

Drilling Fluid:

Oil-Base Emulsion

(Oil with CaCl2 Brine)

Activity = 0.78

TP00-09 43

North Sea Speeton Shale Specimen

Exposed at Zero DP to Drilling Fluid

Drilling Fluid:

Non-Ionic Water-Base

(Methyl Glucoside in

Fresh Water)

Activity = 0.78

TP00-09 44

Principle Mechanisms DrivingFlow of Water and Solute

Into/Out of Shales

Force

Flow

Fluid(water)

Solute(ions)

Hydraulic Gradient (Pw Po)Chemical Potential

Gradient (Amud Ashale)

HydraulicDiffusion

(Darcy´s Law)

Advection Diffusion(Fick´s Law)

ChemicalOsmosis

H2O

H2O H2O

H2Ot1

t2

t3

P

r

Other Driving Forces: Electrical Potential GradientTemperature Gradient

H2O H2O

H2O H2O

H2OH2O

H2O

+ -

-

-

+

+

+

-

TP00-09 45

Osmotic Flow of Water throughIdeal Semi-Permeable Membrane

Ideal Semipermeable Membrane- permeable to water- impermeable to dissolved

molecules or ions

Water flow directionHigh concentration

of dissolved moleculesor ions ( = Low Aw )

Low concentrationof dissolved molecules

or ions ( = High Aw )

TP00-09 49

TP00-09 50

Limitations of Existing Models

Do not handle shale hydration

Very complex

Input data not available

Limited field verification

Cannot field calibrate

TP00-09 51

Mathematical Algorithms

Dr Martin Chenervert (Un. Texas)

Dr. Fersheed Mody (Baroid)

Jay Simpson (OGS)

Dr. Manohar Lal (Amoco)

Dr. Ching Yew (Un. Texas)

TP00-09 52

Mechanical/Chemical Property Input

TP00-09 53

Help Information as Clicking Question Mark

TP00-09 54

Pore Pressure Input/Predict

TP00-09 55

Pore Pressure Predictionvia Interval Transit Time Log Data

TP00-09 56

In-Situ Stresses Input/Predict

TP00-09 57

Correlation to DetermineHorizontal Stresses

TP00-09 58

Output Windows

TP00-09 59

Safe Mud Weight vs Well Inclination

TP00-09 61

Safe Mud Weight Distribution by Azimuth

TP00-09 62

Near-Wellbore Stresses Distribution

TP00-09 63

Mohr Diagram

TP00-09 64

Wellbore Stress Distribution

TP00-09 65

Propagation of Swelling Pressure

TP00-09 68

Too large inclination

Wellbore Stability Design (continued)

TP00-09 69

Wellbore Stability Design (continued)

Decrease inclination

TP00-09 70

Wellbore Stability Design (continued)

Too high mud weight

TP00-09 71

Wellbore Stability Design (continued)

Decrease mud weight

TP00-09 72

Not enough salinity

Wellbore Stability Design (continued)

TP00-09 73

Increase salinity

Wellbore Stability Design (continued)

TP00-09 74

Wellbore Stability Design(through Mud Weight-Salinity diagram)

Too low mud weight

TP00-09 75

Wellbore Stability Design (continued)

Increase mud weight

TP00-09 76

Wellbore Stability Design (continued)

Not enough salinity

TP00-09 77

Increase salinity

Wellbore Stability Design (continued)

TP00-09 78

Wellbore Stability Design (continued)

Low Value Membrane Efficiency

TP00-09 79

Wellbore Stability Design (continued)

High Value Membrane Efficiency

TP00-09 80

Field Calibration

TP00-09 81

Field Calibration (continued)

TP00-09 86

Project Tasks

Distribute Wellbore Stability Model (WELLSTAB)

Develop Enhanced Model (WELLSTAB-PLUS)

Add time dependent feature to model

Hold workshops

Conduct field verification tests

Write technical reports

TP00-09 87

Field Verification Goals

Determine model accuracy

Improve mathematical algorithms

Field calibrate model

Make models more user-friendly

Convert wellbore stability from an art into a science

TP00-09 89

TP00-09 90