Applied Geomechanics_class Notes

8/14/2019 Applied Geomechanics_class Notes

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Vivek Cheruvathoor Applied Geomechanics 2013

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Applied GeomechanicsVivek Cheruvathoor

R10471683

Day 1

Stress and strain

The term stress is used to express the loading in terms of force applied to a certain cross

sectional area of an object,(e.g material , metal, plastics , ceramics , geomaterial etc.].

There are two types of stresses

1. Normal stressForce is perpendicular to the area.

2. Shear stressForce is parallel to the plane

Breakdown stress

Where


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Tensile stress

SvMax vertical stress

Pp- Pore pressure

Direction of stress

The internal force of reaction acting on a small area inside of a plane can be resolved into 3

components.

1. One normal stress perpendicular to the plane

2. Two shear stress components parallel to the plane.

These stresses are average stresses as the area is finite.But when the area is allowed to

approach to zero, The stresses become stresses at a point .

=F/A ; =F/BSince stresses are defined in relation to the plane that passes through the point under

consideration, and the number o f such planes is infinite , there appears on infinite set of stresses

at a point .

fortunately it can be proven that , stresses on any plane can be computed from the

stresses on three orthogonals (i.e perpendicular to each other) passing through that point.

As each plane passing thru the point has stresses ( 1 normal and 2 shear) the stress tensor has 9

stress components which completely describe the state of stress at a point .The 9 stresscomponents are expressed in matrix form as follows.

v

h

H


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[ ]This is in three dimensions . In two dimensions we have 4 stress tensors, the z component

vanishes.

For steel , the relation between stress and strain is given below

In rare cases, the principle stresses may not be vertical or horizontal.

e.g1

. Offshore Louisiana field (near Colombia ).

2. Some parts of Gwahar field ( Saudi Arabia).

Summary and conclusion

1. External applied force can create internal (reaction) forces which may generate

strain in the material. If the material is constrained in space, Internally or externally.

2. We have at any point in the material subjected to external or Internal forces.


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06/05/2013

Transverse fractures

How It often should be placed

1. Economic concern

2. Is it geo-mechanically possible .

Area of concern

For drillers : For Hyd Fracturing:

In-situ Stresses

For Drillers - R concern = 4 X Well radius

For Hydraulic FracturingRconcern = 100- 200 X well Radius

- Present maximum number of stages in a single well200 stages.

Poroelastic theory

- Increased pore pressure causes decreased effective stresses.

- Increased stress by reducing the stress sand broken into small pieces .

R concernR concern


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Bradley and risnes

Elastic Moduli

- Rocks mechanical characterictic properties (parameters) are defined by following two

independent parameters ( broadly called elastic moduli)

- Youngs modulus of Elasticity

- Poissons ratio


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It is an intrinsic property changing with temperature. But there exists 2 other elastic moduli which are

not independent properties but related to E&, This relationship are derived from the first principles of

physics by solving the wave equation.

Wave equation is based on conservation of mass , Energy and momentum

Types of Elastic Moduli

Based on the method of measurement there are two types

1. Static elastic moduli - Classical core testing.2. Dynamic elastic Moduli - Ultrasonic testing, Field seismic survey.

Types of seismic waves

1. Compressional wave (Vp)

2. Shear wave(Vs)3. Rayleigh wave (Vr)

4. Love Waves (VL)

[pic]

Hydraulic fracture is tensile fracture.


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The measured value of both depends on the ratio of loading . It is better expressed as strain ratei. Less than 10-2/ second is called static on quasi-static method. [ civil and other engineers

developed ASTM test method in this rates.

ii. 10-1to 101/sec => High rate of strain ( Ultrasonic seismic)

iii. 101

to 102

/ second => very high rate of strain.iv. 104and upwards => Ultra strain rate [ Loading by explosives , propellant]

- Explosive loading creates low permeability around bore hole if no permeability.

Assignment : Relationship between Elastic Constants

06/06/13

- American Rock Mechanics Associationwww. Armarock.org.

Stress Concentration

- Both compressive and tensile stress

- Stress concentration is very important inorder to understand how in-situ stresses atgreat depth change in both magnitude * stress concentration by way of concentration+ near

the borehole as soon as rock excavation by drill bit takes place and direction.

The bore hole wall so long been supported by rock that is now removed . This causes stress

concentration.

Plate example:


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Stresses will be concentrated around the bore hole because of combined effect of forces related toMathematically the concentrated stress distribution can be obtained by the principle ofsuperposition.

Direction of hoop stress is given by azimuth.

Stress at (A,A) (B,B) stresses are no longer but the product of 3 others newly createdstresses by they are


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All are functions of & (r,rw)Stresses are always associated with a plane

However small in regards to point stress

In 3D , this stresses are 1) Normal 2) Shear.

In 2D , we will have one normal and 1 shear stress . Considering mathematical relationship of with the applied forces.

xyand yx must be equal .

We are interested to find on any arbitrary angle and y-axis.ncan be shown by principle of equating forces.

( ) ( )

( )Principal =0


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tan-1 (

in the equation for Nwe get both the magnitude & direction of the principal stress. So principal stress

refers to normal stress acting on the plane imaginary on fracture plane on which there exists no shear

stress .

Implication or significance of principal stresses

1. make easy rock failure calculation (modeling)

2. In borehole fracturing , the fracture grows in the direction of minimum principal stress . That

means there exists there exists no shear stresses on the newly created fracture surfaces.

What if we create fracture surface in any other directions .

There will be shear stress.

Due to pressure shear stress on both fracture faces ,

These surfaces tend to be slightly displace laterally but parallel to each other . This is called shear

displacement. Which civil engineering researchers have measured in lab experiments.


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Q. Is shear displacement significant for Petroleum Geomechanics Application (Eg. Fracture Stimulation)

A. Yes, Because CE have measured this shear displacement to be the ordered of 0.20.8 mm . It may be

possible to keep fractures open without proppant if the fractures could be created in non principal

stress directions.

Q. Any proof? (Lab, Oilfield)

A. Yes, special studies using Dynamic fracturing method.

e.g propellant -> shock wave in borehole.

-> Stress wave in formation rock.

-> creates 5-10 radial fractures .

The ones in non-principal stress direction remain open.

To find the In-situ stresses

1. 2.

Pic.

At A A and B B are points on the well bore.

Example:

If


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If

[pic]

Sedimentary deposit in basin


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06/12/2013

Weve approximately learned stress distribution equation around a vertical well bore .But how can we

tell (quatitatively ) if the well bore is in or near a state of failure?

In borehole stability analysis (especially in drilling) we define failure to betensile or shear failure from

GM.

Procedure (Vertical Well )

1. At depth interval of interest , generate distribution (say using excel)2. Using the data from step 1 , construct Mohrs circle representing shear stress conditions on

borehole wall @ . (0 => Direction of Hmax).3. From Lab Experimental data (Triaxial conditions ) , construct Mohrs circle failure envelope.

4. Change Pwvalues until you find the Mohr circle at = 0exceeding the tensile strength value. [

This is initiation of hydraulic fracture, if fracture length is long borehole fluid will get lost => it


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may lead to lost circulation -> blowout [ if the formation interval is permeable] [ if formation

bears high pressure fluid]

5. It gives maximum available mud weight.

[pic]

Coloumb friction theory

Mountain peg

Where

So= cohesion

= coefficient of internal friction.

As Nincreases increases


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When -> o(Shear strength of rock ) then shear failure takes place. Sinceis arbitrary so for a

particular value of , the owill be reached first that is called angle of failure.

Q. How do you increases Nto make also increase and reach 0


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A. In civil , mining and petroleum field of study encountered increase in compressive load . That is

compressive loading leads to shear failure . In literature compressive failure is equivalent to shear

failure.

Q. Is Coulombstheory of friction valid for all ranges of stress?

A. No in 1900, Mohr stated that CTF id valid when the confining stress is low as in most civil and mining

application

He found that the failure curve or envelope is non linear of the generic form= f(). This is called Mohrs

hypothesis. Therefore if we can develop using experimental data an expression for f() , it is possible to

graph the failure curve like this

Q. How do we generate the sets of experimental data by triaxial test

A. Take 5+ identical core plugs from your reservoir rock or overburden formation. Either cut in vertical

direction or horizontal direction. Do a triaxial test on each at various confining pressures. (Pc or 3).

Sample Pc Sigma

1 0 3000

2 500 3300

3 1000 3500

4 1500 3700

5 2000 39006 2500 4100

Point of tangency P represents the shear strength oof the sample of the core at confining pressure = Pc

(3)

For the first case


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Identify the failure point on each Mohr circle and connect these points by a curve you get Mohrs failure

curve. Ideally it is a cubic equation . Fit a trend line through the points it will be a polynomial of the

third order power law.

Ref J.C JagerFundamental of rock mechanics

Quality control on Mohr failure curve

1. Have relable To and Co values experimentally

2. The Mohr failure curve should pass through (To,0) and also become tangent to Mohr circle

corresponding to UCS data points.

Borehole well stress analysis

Griffith theory of fracture- fracture mechanics.


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06/19/13

Team 1 : Clark and Indra

Team 2 : Suraj and Sergio

Team 3 : Sudarshan and Raymond

Team 4: Abdul and Misfer

Team 5 : Aman and Marshal

Team 6: Vivek

Team 7 : Valentine

Lab experiments # 2 and 3

Determine UCS (Co) and tensile strength (Brazilian disc) of

1. Portland cement

2. API Cement class H

After a curing period of

a. 24hoursb. 7hours

Number of samples to be prepared

Type of cement Test type 24- hours 7 days

Portland CementUCS 1+1 1+1

Tensile 1 1

API Class H cementUCS 1+1 1+1

Tensile 1 1

Total 6 6

In UCS test one sample is tapped other sample untapped.Totally make 12 samples.

Time taken

1. Weighting and adding5 min each group

2. Mixing15 min each group


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Procedure

For each type of cement , do as follows,

Part 1 (Slurry preparation and molding)

Step 1: Using a water to cement ratio = 0.5 , estimate the weight of dry cement powder and water

needed to make 15 samples.

12+3 = 15 samples

Bring the calculation sheet filled up

Step 2: Use a blender to prepare slurry

Step 3: Cast in 6 cylindrical molds given. Tap 50 times 4 samples , leave 2 samples untapped

Step 4: Go to step 1 using class H cement.

Part 2 (curing)Step 1: In a humid or moist environment, cure 2+1 samples for 24 hours. Cure the other 2+1 samples for

7 days.

Ideally, Curing environment should be as close as the in-situ conditions in

1. Bottom hole pressure

2. Down hole temperature

3. Porefluid interacions

Part 3 ( Experiments)

a. UCS test ( As per ASTM C39)b. Brazilian disc test (As per ISTM Standards mentioned in the blue book)

The disc thickness for Brazilian disc test is 1 cm.

Hoek Cell

It is a pressure cell used to carry out compression test at various confining loads. The maximum

confining load is usually 20000 psi.


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Hydrostatic stress

In geomechanics terms, the hydrostatic stress refers to the average of all principal stresses

Where as hydrostatic pressure refers to the pressure due to the hydrostatic column of fluid

Volumetric shrinkage

At high depth and at nominal tectonic stress, all the three stresses will be equal.

This causes the rock to shrink without tensile or shear failure.

In many locations around the world much of the permeability of carbonate rocks comes from natural

fracture networks connecting vugs present in oolitic lime stones.


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Super K project

Super-k (carbonate zones of extremely high permeability) can significantly enhance recovery per well in

the Ghawar Field. This research project has three objectives. The first objective is to identify and

characterize super-k zones. The second objective is to identify chemical blocking agents that can be

placed in super-k zones without reducing hydrocarbon productivity. The third objective is to identify an

effective technique to optimize the size and the placement of the chemical blocking agents.


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After taking the new cross section the stress is recalculated. The maximum allowed reduction in cross

section is 2% offset.

For example in J-55 tubing , the minimum yield stress in 2% increase in permanent strain rate after the

maximum yield strength

06/20/13

Well bore instability

Please study the paper SPE mohiuddin , Awal (2002)Zuluf field Instability.

Definition of borehole instability.

BHI means one or more of the following symptoms

1. Tight hole => Increased torque

2. Hole pack off => difficulty in Pulling out (POOH).

3. Lost hole => Difficulty in Running in the hole (RIH)

Please note that this BHI occurs mainly in overburden rock drilling and world over, about 60-75

% of the overburden rock is shale.

Reasons for tight hole

1. After drilling through a shale zone, slip has occurred .

2. Insufficient hole cleaning of drill cuttings and shale

cavings.

3. Barite sag in deviated holes.

[Picture]

Need to carry out CFD analysis on bore hole liquids

There may be reasons for tight hole other than Geomechanics

Hole packoff due to cuttings and cavings (shear failure)


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Shales are most of the time fractured. (incipient microfractures). But due to overburden pressures, They

are healed.

while drilling . After 10-20 hrs of exposure the pressure adjacent to the wellbore increases. Wecall it Mud pressure Penetration.

Formation damage comes into picture only when drilling through payzone.

Avalanche effect

When avalanche of cutting bed happens, There will be no circulation, you cannot rotate and you cannot

pullout.

Normally avalanche occurs at well deviation from 45-65 degrees.

How to avoid avalanche effect?

1. This effect is more severe when drilling through shale formations.So for conventional drilling ,

Find the shortest path possible through shale.

2. Drill through shale in the shortest possible time.

3. Use short radius wells to avoid 45-65 degrees window where avalanche effect is prominent

[Pic]

4. Do back reaming using a reamer in the drill string whenever possible.


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Hydromechanical cleaning (hydroclean)

VAM Drillings patented Hydroclean is a Hydro-Mechanical Hole Cleaning Device (MCD)uniquely designed to increase hole cleaning efficiencies while drilling primarily large holesections of in highly deviated wells. The tool features fit-for-purpose bladed scallops andgrooves producing a number of hydro-mechanical effects resulting in drilling performanceimprovements.

Exam Review

Section 1 : Stress strain + Mohr circle + Rock failure

Criteria 1. Mohrs failure envelope 2. Mohr coloumb

Section 2: Application 1. Drilling Instability 2. Fracture stimulation.(Hydraulic fracturing)

Only fracture initiation Construct Mohrs circle.

Hydraulic fracturing


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Pw corresponds to Mohr-

circle intersecting the MFE on the tension part is called formation breakdown pressure Pbt. i.e toinitiatie hydraulic fracture the bore hole pressure must reach Pbr.

Final ExamJuly (9-12)

But to propagate the incipient fracture to desired frac half length specially formulated frac fluid vol must

be injected at pressures which is slightly less than Pbr(Pf


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If there is not well bore pressure penetration. At fracture closure pressure , the pressure at the bottom

hole = h

In retrospect , the pressure vs time analysis tell us that if we stop pumping after 2-5 min , we can get

more accurate values of To and h which now can be used to improve the hydraulic fracture design and

also get Cl( fluid leakoff coefficient) which is vital parameter in designing the pumping schedule for

hydraulic fracturing . this test is called minifrac test.

This pre-frac injection test is called a minifrac test.

Complete operation sequence in a hydraulic frac treatment.

1. Minifrac test

2. Mainfrac operation which has

a. Pad vol inj

b. Proppant slurry

3. Postfrac analysis

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Applied Geomechanics_class Notes