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1. INTRODUCTION Large oil and gas reservoirs are associated with salt structures. Domal structures in the Gulf of Mexico (GoM – Jurassic salt emplaced during the Tertiary), Williston basin (Mid US Continent Devonian age)  the North Sea (Zechstein age salt emplaced in the Cretaceous), Iran (Zagros salt plugs, which in some areas outcrop), Brazilian and West African offshore  basins, and other areas, provide targets for exploratory o il and gas drilling. Sub-salt resource s are found in the GoM salt tongue regions, in large areas in Kasakhstan (Kashagan and Tengiz), and in other areas. These may involve drilling throug h as much as 1500-2500 m of salt to depths of 5-9 km. Drilling through salt is rapid if there are few non- salt beds. Typical ROP of 15 to 40 m/hr me ans that a 1000 m section can usually be drilled in two or three days with a PDC bit. ROP is important  because speed minimizes hole closure from creep. Salt is essentially impermeable, so the effect of drilling fluid density (MW) on ROP is small. MW management can be used to control closure rate while sustaining reasonable penetration rates. However, high MW carries risks of lost circulation in non-salt zones, and this risk must be properly managed through knowledge of stresses. Salt does not present as serious drilling problems as fractured shale, but there are challenges such as washouts, rapid borehole closure, mud weight con- trol issues, and c asing placement dec isions. Subsalt overpressure or pressure reversion may exist, and extensive rubble or sheared zones are common underneath salt tongues or adjacent to diapirs. It may be difficult to decide where salt ends and non- salt sediments start: salt-infilled rubble zones and salt with 30-40% non-salt shale and sand inclusions can exist within salt beds, or at the boundaries of salt s tructures. However, most d rilling pr oblems within salt are managed relatively easily by considering salt properties during planning and drilling. Issues arising in d rilling around salt structures are discussed elsewhere [1]. Salt is found as salt tectonics structures (domes, ridges, salt tongues, pillows…) as undeformed  bedded sedimentary salt, and as mixed domains, as in the GoM, PreCaspian Basin, South Atlantic margin basins (Brazil, Angola…), Canadian Scotian Shelf and the Central Graben area and more southern parts o f the North Sea. Because of visco us  behavior at modest stresses and temperatures, salt can be tectonically mobilized solely because of density differences between salt (2.16 g/cm 3  for  pure NaCl) and other sediments (2.3 – 2.6 g/cm 3 ). DRILLING THROUGH SALT: CONSTITUTIVE BEHAVIOR AND DRILLING STRATEGIES Maurice B. Dusseault GEOMEC A.S. and Porous Media Research Institute, University of Waterloo, Waterloo, Ontario Canada, N2L 3G1 Vincent Maury GEOMEC A.S., 12 Avenue des Pyréneés, 64320 IDRON, France Francesco Sanfilippo GEOMEC A.S., Via Cairoli 106, Casalmaggiore (CR), 26041, Italy Frédéric J. Santarelli GEOMEC A.S., Olav Duuns gate 12, Stavanger N-4021, Norway ABSTRACT: Drilling through salt sections requires that the particular properties of salt, its creep behaviour and high solubility,  be recogniz ed and incorpora ted in the dril ling plan. Salt is a vi scous material and creeps unde r differentia l stress; the cree p rate is a strong function of both temperature and stress difference (actually underbal ance between the mud pressure and the vertical stress). A simple model approach to account for these effects in a reasonably quant itative manner is described. Problems encountere d in drilling through salt include hole closure leading to stuck tools, differential dissolution of beds of carnallite, bischofit e and other halides, encountering stiff and non-viscous stringers in salt strata, and exiting salt into non-salt rocks, always a challenging phase of the drilling. Strategies for successful salt drilling involve recognizing salt closure behavior, stresses, and adjusting drilling fluid densit y and temperature to minimize probl ems. Casing design issues in salt are also discussed.
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1.  INTRODUCTION

Large oil and gas reservoirs are associated with salt

structures. Domal structures in the Gulf of Mexico

(GoM – Jurassic salt emplaced during the Tertiary),

Williston basin (Mid US Continent Devonian age) 

the North Sea (Zechstein age salt emplaced in theCretaceous), Iran (Zagros salt plugs, which in some

areas outcrop), Brazilian and West African offshore

 basins, and other areas, provide targets for

exploratory oil and gas drilling. Sub-salt resources

are found in the GoM salt tongue regions, in large

areas in Kasakhstan (Kashagan and Tengiz), and in

other areas. These may involve drilling through as

much as 1500-2500 m of salt to depths of 5-9 km.

Drilling through salt is rapid if there are few non-

salt beds. Typical ROP of 15 to 40 m/hr means that

a 1000 m section can usually be drilled in two or

three days with a PDC bit. ROP is important

 because speed minimizes hole closure from creep.

Salt is essentially impermeable, so the effect ofdrilling fluid density (MW) on ROP is small. MW

management can be used to control closure rate

while sustaining reasonable penetration rates.

However, high MW carries risks of lost circulation

in non-salt zones, and this risk must be properly

managed through knowledge of stresses.

Salt does not present as serious drilling problems asfractured shale, but there are challenges such as

washouts, rapid borehole closure, mud weight con-

trol issues, and casing placement decisions. Subsalt

overpressure or pressure reversion may exist, and

extensive rubble or sheared zones are commonunderneath salt tongues or adjacent to diapirs. It

may be difficult to decide where salt ends and non-

salt sediments start: salt-infilled rubble zones and

salt with 30-40% non-salt shale and sand inclusions

can exist within salt beds, or at the boundaries of

salt structures. However, most drilling problems

within salt are managed relatively easily byconsidering salt properties during planning and

drilling. Issues arising in drilling around saltstructures are discussed elsewhere [1].

Salt is found as salt tectonics structures (domes,ridges, salt tongues, pillows…) as undeformed

 bedded sedimentary salt, and as mixed domains, asin the GoM, PreCaspian Basin, South Atlantic

margin basins (Brazil, Angola…), Canadian Scotian

Shelf and the Central Graben area and more

southern parts of the North Sea. Because of viscous

 behavior at modest stresses and temperatures, saltcan be tectonically mobilized solely because of

density differences between salt (2.16 g/cm3  for

 pure NaCl) and other sediments (2.3 – 2.6 g/cm3).

DRILLING THROUGH SALT: CONSTITUTIVE BEHAVIOR AND

DRILLING STRATEGIES

Maurice B. DusseaultGEOMEC A.S. and Porous Media Research Institute, University of Waterloo, Waterloo, Ontario Canada, N2L 3G1

Vincent MauryGEOMEC A.S., 12 Avenue des Pyréneés, 64320 IDRON, France

Francesco Sanfilippo

GEOMEC A.S., Via Cairoli 106, Casalmaggiore (CR), 26041, ItalyFrédéric J. SantarelliGEOMEC A.S., Olav Duuns gate 12, Stavanger N-4021, Norway

ABSTRACT: Drilling through salt sections requires that the particular properties of salt, its creep behaviour and high solubility, be recognized and incorporated in the drilling plan. Salt is a viscous material and creeps under differential stress; the creep rate isa strong function of both temperature and stress difference (actually underbalance between the mud pressure and the verticalstress). A simple model approach to account for these effects in a reasonably quantitative manner is described.

Problems encountered in drilling through salt include hole closure leading to stuck tools, differential dissolution of beds ofcarnallite, bischofite and other halides, encountering stiff and non-viscous stringers in salt strata, and exiting salt into non-saltrocks, always a challenging phase of the drilling. Strategies for successful salt drilling involve recognizing salt closure behavior,

stresses, and adjusting drilling fluid density and temperature to minimize problems. Casing design issues in salt are also discussed.

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Figure 1 shows cases ranging from shallow bedded

salt to deep diapiric structures. In salt tongues

(sheets) and bedded salt cases, well trajectory

choice is limited, but with diapiric structures, a wide

range of drilling trajectory choices exists, including paths which avoid salt altogether, and other paths

designed to pass through as much salt as possible.

Which is chosen depends on the geomechanical

state of the rocks surrounding the salt, the depth (T,

σ) and creep rate of the salt, and other factors, some

experiential, some gleaned from analysis.

Assuming that salt dissolution issues in the drillingfluid are properly managed, the two major concerns

are borehole closure through creep, and borehole

instability when exiting salt or in cases of sharp

lithology contrasts (e.g. anhydrite/salt interfaces).

Casing point choices must account properly forstresses so that drilling can proceed at low blowout

and lost circulation risk.

To manage drilling risks, it is necessary to:

•  Determine the in situ conditions, T(z), σ(z)

•  Choose a suitable constitutive law for creep

•  Calculate borehole closure rates as functions of

depth and activating stress (σv – p b)

•  Assess the risks and if necessary executethermal (cooling and heating) calculations

•  Choose the best mud weight program for thecasing program and trajectory

•  Monitor hole performance and be prepared to

modify the program appropriately

•  Be prepared to act decisively when exiting thick

salt structures.Figure 1 (Left and Below): Some Conditions Encountered in

Drilling Salt

2.  IN SITU CONDITIONS

2.1.  Stresses and TemperaturesFigure 2 shows a profile of a thick salt tongue in the

GoM. The temperature is ~0°C at the sea floor, and

~80°C at 5.5 km subsea. In the cases sketched in

Fig 1, the geothermal gradient is on the order of 20-

25°C/km, typical values for sedimentary basins, butthere is a lower geothermal gradient, on the order of

15°C/km in the GoM deep offshore area. These

low T gradients facilitate salt drilling, compared to

 North Sea cases where gradients within salt

approaching 38°C/km have been found. 

Because salt rocks are viscous and flow slowly at

all non-zero shear stress states, one may assume that

σv  = σHMAX  = σhmin  = ⋅γ   , where γ     is the mean

overburden bulk density. Careful measurements in

mines and LOT or FIT values obtained during salt

drilling all tend to confirm this condition. Isotropic

stresses are only found in viscous rocks and very

Z - km

1

2

3

4

Sheared salt,

shale, anhydrite

Carnallite zone

Differentwell paths

Residuum

gas,

oil

GoM Salt Diapir b)

Z - km

1

2

3

4

Sheared salt,

shale, anhydrite

Carnallite zone

Differentwell paths

Residuum

gas,

oil

GoM Salt Diapir b)

Igneous bedrock

500

1500

1000

   Z   (  m   )

T (ºC)10 20 30 40

a)Eastern Alberta

Bedded salt zones

Igneous bedrock

500

1500

1000

   Z   (  m   )

T (ºC)10 20 30 40

a)Eastern Alberta

Bedded salt zones

   Z   (   k  m   )

0

1

2

3

4

Weak Tertiary and

Cretaceous clastic

sequence

Strong Jurassic and

Triassic siltstones,

carbonates, snds

Thick salt beds,

brine pockets

Subsalt sediments,

po ~ 17 kPa/m

Kungurian

Salt Beds

c)North Caspian

Basin Sequence

100ºC

   Z   (   k  m   )

0

1

2

3

4

Weak Tertiary and

Cretaceous clastic

sequence

Strong Jurassic and

Triassic siltstones,

carbonates, snds

Thick salt beds,

brine pockets

Subsalt sediments,

po ~ 17 kPa/m

Kungurian

Salt Beds

c)North Caspian

Basin Sequence

100ºC

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soft mud; in frictional materials such as sandstone,

limestone and shale, the in situ stresses are

invariably unequal. Because salt is a viscous liquid,

the term under-balance is used herein to mean a

mud pressure less than the vertical stress p b < σv.

Figure 2: Thick Salt Sheet, Deep Offshore GoM

The vertical stress is plotted with depth in Fig 2 as asolid line, as well as dotted lines for pressures that

would be applied from a borehole full of a static

fluid. When an offshore deep water borehole is full

of a drilling fluid and penetrates a large sequence of

salt, it is not possible to equilibrate the stresses bydrilling mud pressure at both the top and bottom of

the salt. Suppose one wishes to balance the stress

while drilling at the base of the salt to avoid all

creep; when the fluid is static at ρ = 1.8 g/cm3, there

is a surplus pressure at the top of the salt sequence

of >10 MPa. But, if it is necessary to stay below

the fracture pressure in the soft sediments at the top

of the salt, for which a 1.3-1.4 g/cm3 mud would be

used, there would be >18 MPa underbalance (σv  – pw) at the salt base, and creep closure would be an

issue, especially with high T cases. It is best, in

most circumstances, to place a casing shoe into the

salt as far below the salt top as possible.

This discussion shows that a high creep rate

 potential exists and it is difficult to balance the rock

stresses in deep water conditions (leaving aside

technologies such as sea-floor booster pumps or gas

lift). Thus, closure rate potential must be evaluated

to see if borehole closure is a potential problem.

Direct well closure rate measurement the best

approach to determine creep rate (rather than

laboratory measurements on cores). Running

successive caliper logs is feasible, but expensive. It

is best to monitor tripping conditions during bit trips

and short trips, and Fig. 3 illustrates this for a North

Sea well drilled with OBM. It shows a periodic

recurrence time for critical closure with the chosenmud weight. In some regions (Williston Basin),

critical periods as small as 1 hour have been

reported in dirty salts – i.e. rich in clay – making

drilling almost impossible.

Figure 3: Salt Closure, North Sea Well. Black bars represent

 back-reamed sections while tripping.

2.2.   Permeability and Pore PressuresUnder stress, sedimented granular salt continues to

compact, expelling brine, until porosity is totally

occluded (φ  < 2-4%). Even after this, particularly

with high stresses and temperatures, salt continues

to compact until a brine-filled porosity of 0.3-1.5%

remains. This consists of thin, dendritic voids at

grain boundaries, but for practical purposes, salt permeability can be taken as zero. Flow through

salt in engineering time scales (<100 years) occurs

in non-salt lithologies or through introduced flaws

(e.g. hydraulic fracture). A filter cake cannot form,

and 100% of the mud pressure acts directly on the

salt. The same is assumed of rocks where pores are

filled with precipitated salt: there is no inter-communicating flow path, therefore the concept of

 pressure as a state descriptor is not useful.Though fluid flow and pore pressure concepts are

not applicable to salt, brine pockets can be

encountered, sometimes with po approaching σv. In

 bedded salts of lithostratigraphic complexity, there

can be non-salt zones where porosity is filled with brine that can enter the well. Estimating po in brine

 pockets is impossible; in our experience, in a typical

sub-Zechstein field, brine pockets from 1 to 2.2

equivalent SG pressures can be encountered during

drilling. Brine kicks and gas inflows in intact salt

sequences are often of small volume and generally

inconsequential, but  high pressure brine pocket 

0 50 100

Stress, pressure, MPa

0

H2O, ρ ~ 1.025

Soft seds, ~ 1.9

Salt, ~ 2.16

Sub-salt sediments

1.2 g/cm3

1.4 g/cm3

1.6 g/cm3

1.8 g/cm3

σv

Fluid pressures

   Z   (   k  m   )

1

2

3

4

580ºC

σh

0 50 100

Stress, pressure, MPa

0

H2O, ρ ~ 1.025

Soft seds, ~ 1.9

Salt, ~ 2.16

Sub-salt sediments

1.2 g/cm3

1.4 g/cm3

1.6 g/cm3

1.8 g/cm3

σv

Fluid pressures

   Z   (   k  m   )

1

2

3

4

580ºC

σh

Drilling Days – Zechstein Salts

14

15

16

17

   D  e  p   t   h

   (   ‘   0   0   0   f   t   )

0 5 10 15 20 25Drilling Days – Zechstein Salts

14

15

16

17

   D  e  p   t   h

   (   ‘   0   0   0   f   t   )

0 5 10 15 20 25

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kicks in Pakistan led to casing collapse and surface

 brine flow for many years.

3.  A CONSTITUTIVE MODEL FOR HALITE

Since chances of obtaining salt core and performingcomprehensive constitutive testing are exceedingly

rare, to analyze borehole closure rate it is necessary

to adopt a constitutive law that captures first-order

 processes, yet is simple enough to be used in

sensitivity studies with field calibration.3.1.   Minerals in Salt Strata

 Natural “salt” deposits are usually pure NaCl

(halite) crystals of 1 – 20 mm mean grain diameter

with 0-15% insoluble materials such as shale beds

or intercrystalline clay (“chaotic salt”). Deep

 bedded salts (>2000 m depth) and all diapiric or

tectonically mobilized salts have undergone

recrystallization. Non-salt mineral content is lower

and the crystalline fabric more uniform, withcrystals of 5 mm to 10-20 mm. Other halides may

exist in beds of limited thickness and extent, such as

the 3-6 m thick “potash” beds of ~50% KCl, ~50%

 NaCl being mined in Saskatchewan and elsewhere.

Sylvite (KCl) behaves similarly to halite, but therecan be beds, streaks or mixtures of carnallite,

 bischofite, tachyhydrite, polyhalite, and other rarehalides. When encountered, they can present

 particular difficulties; coping with such cases is

discussed later.

Thin streaks of shale or other halides is of great

interest in mining, where pillars can be seated on

other mineral types, or where differential strain

rates in roof strata lead to slab detachment and roof

falls. In drilling, these minerals may not cause

 problems if zones are thin as they tend to be weakand soft so that it is easy to sustain a borehole and

to back-ream if hole gauge problems develop. Anexception may develop in chaotic salt, where even

small creep closures lead to debonding and

sloughing of chunks of clayey salt into the borehole.

In drilling with NaCl-saturated WBM, non-salt

zones are preferentially dissolved because the

aqueous fluid is not saturated with respect to them,

and this dissolution tends to counteract any squeeze.

Hole enlargement issues may arise in these zones,

or else they will have to be redrilled when runninginto the hole, and such redrilling takes only a few

minutes. However, mud properties may change

dramatically, especially if Ca++  or Mg++  cation

halides are encountered. Thus, the creep behavior

of other halides is generally of secondary interest,

and one may focus on the creep behavior of NaCl.

If there are difficulties associated with rapid closure

of a zone of non-NaCl halide minerals, the only

 practical method of reducing the problem is to raise

MW to a level close to the stress to reduce creep.

3.2.   Halite (NaCl)Halite (NaCl) is a natural mineral deposit of low

 porosity; this low porosity is brine-filled, and the

 brine plays an important role in creep behavior.

Before 1975-1985, salt creep was modeled with

empirical equations, such as a fractional time

exponent (e.g. a At =ε & ), to emulate triaxial tests

and model pillars or field data. These non-physical

equations lumped all phenomena in one term so

different processes could not be deconvolved. Forexample, in a mine creep leads to pillar widening

and thus slowing of the closure rate (creep stress is

reduced). Empirical equations based on such data

cannot lead to a physically correct constitutive law

 because macroscopic creep is a function of

constitutive behavior combined with geometry and

stress changes. It is now clear that these must betreated separately and correctly, using continuum

mechanics approaches [2].

Pursuit of a physics-based constitutive law for salt

has been quite successful, though in complex cases(e.g. salt/shale mixtures, mineralogical complexity,

small-scale heterogeneity) substantial uncertainty

exists. The major aspects of the physics of salt are

discussed in order to rationalize the model used.

At conditions encountered during salt drilling (T =

10-150°C, σv - p b = -10 to +30 MPa), lattice bonds

in halide minerals are strongly ionic, whereas bonds

in most minerals (quartz, feldspar, calcite) are

covalent. Only at high temperatures are ionicenergies overcome and can lattice deformations take

 place in a dry polycrystalline material without

accumulating damage. Processes involved in high

temperature creep, within 10-20% of the melting

temperature (in °K) do not have to be considered in

drilling, so these mechanisms are irrelevant.

A single dry salt crystal shows no transient creep

 behavior. Once some stress threshold is exceeded,

dislocation glide and climb within the lattice

dominate creep. If the applied stress is high, the

dislocation processes evolve rapidly toward the

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generation of Griffith cracks, leading to

accumulating damage, and perhaps weakening.

An assemblage of salt crystals evidences complex,

self-organized behavior because of the structural

interaction of crystals and boundaries, and because

of the presence of water. Transient creep occurs

whenever stresses are changed because external

loads must be distributed at the lowest energy state

within the crystalline structure, which takes time

(strain). Also, transient creep is larger when there is

damage, as in microfissured core specimens(because of de-stressing during coring). In a

 borehole, transient behavior occurs for a short time

after drilling, and damage level is minimal because

a high σr   continues to act on the salt from the

drilling fluid. Transient creep during drilling can be

ignored: it is attenuating and inconsequential.

Because of brine in the non-connected intergranular

 porosity, a process known as FADC (fluid-assisted

diffusional creep) affects salt creep over a T and σv 

range typically found during drilling. FADC

appears to be a critical component of the

mechanisms that dominate creep, and these involve

salt dissolution at highly stressed points, diffusionaltransport, and precipitation in regions of low stress,

thereby allowing for simultaneous mass transfer andstress equilibration. If an external deviatoric stress

is maintained, as in the vicinity of a borehole where

 p b ≠ σv, steady-state creep continues as long as the

crystalline fabric of the salt rock remains the same.

Because creep distortion is modest (∆r/r < 20%),

given that a borehole remains open for a limited

time, effects associated with change of watercontent or salt fabric are small; it is reasonable to

assume that a physically-based steady-state creep

law will suffice for borehole closure simulation.

In summary, based on our experience and onobservations, we will assume the following:

•  Transient creep strains in boreholes are small

and can be ignored for practical purposes.

•  At conditions encountered in salt drilling,induced damage (microcracks) is of no

consequence because of high confining stress

and the tendency of salt to anneal during creep.

•  Except in chaotic salt, creep failure or strain

weakening will not occur in salt with a

reasonable MW.

•  It is thus sufficient that a constitutive law for

salt account only for steady-state creep.

Fig 4: Several Simple Constitutive Models for Salt

Figure 4 shows several simple rheological models

to represent salt behavior, with the bottom two

showing elements of transient response or multiple

mechanisms (many highly complex models have

 been suggested). We claim that the first model is

sufficient to simulate salt behavior in drilling. Theviscosity η is not Newtonian, nor is it independent

of temperature, but the Young’s modulus may be

taken as constant at 31 GPa and the Poisson’s ratiofor elastic stress changes is 0.36. The viscosity

(steady state strain rate -  ssε & ) is expressed as:

 RT 

Qn

o

b ss e

 p A

⋅ 

  

    −=

σ 

σ ε &   (1)

σ  - p b  is the difference between in situ stress (σv)

and borehole pressure (generally p b  = MW·z),

termed the plastic stress. The Arrhenius thermal

activation term has the activation energy Q for

creep; Q = 95 kJ/mole is recommended for borehole

conditions, though the literature reports values from55 to 272 kJ/mole. Specimens from Avery Island in

southern Louisiana and the Palo Duro bedded salt

from New Mexico gave Q values of 55 kJ/mole and

90 kJ/mole respectively in the temperature range of

25ºC to 200ºC, but European research has tended to

give higher values. Note that different mechanisms

have different activation energies, but we assumethat one dominates. “A” is a constant determined

through calibration, and σo  is a normalizing stressvalue that we commonly take to be 10 MPa.

E  η

E1

E2

E

η1

η1

η2

η2

K

∆σ

∆σ

∆σ

 A

B

C

E  η

E1

E2

E

η1

η1

η2

η2

K

∆σ

∆σ

∆σ

 A

B

C

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Figure 5: Temperature and Creep Rate

In Fig. 5, the effect of T on creep rate is presented.

In general, for one mechanism, the slopes are

assumed to be the same for different stress levels; in

fact, there is a weak confining stress effect, but it is

small and can be ignored (as in Equation 1).

Choice of an exponent n is a highly contentious

issue. Back-analyses from large-scale mine cases

[3.4] lead inexorably to a value of 3.0, no matter

what the theoretical arguments. Similarly, back

analysis of laboratory data for radioactive waste

repository studies [5] suggests that n = 3.0. In amine, there is another faster creep process (stable

microcracking) that does not occur in a borehole

 because of the confining stress of the drilling fluid.

Figure 6: Creep Mechanisms in a σ - T Plot (σ can be taken as

~ σv – p b in a reasonable first approximation)

Fig. 6 shows the T and σ  range in typical drilling

conditions (ellipse), plotted on a mechanisms

diagram (Munson and Dawson data). It appears that

only one mechanism acts in the range of drilling,

therefore a single exponent creep law is justified.

Finally, we note that determining the constant A

independently is laborious [6], thus, in predicting

hole closure rates, experience is required and field

calibration is desirable.

4.  BOREHOLE RADIAL CLOSURE MODEL

4.1. 

The effect of stress ( σ v – pb )A numerical or analytical model that links the

system parameters and the stress difference to the

rate of radial closure is needed to complete thedesign process. In this axisymmetric case it is

 possible to extract a closed-form approximation for

steady-state closure. We use the method developed

 by Bogobowicz et al. for steady-state closure of

openings in non-newtonian viscous materials [7].

( )n

o

bvoo

 p

nr 

 

  

    −=

σ 

σ ε ν 

3

2

3&   (2)

Here, vo is the borehole closure rate, n is taken to be

3.0, and oε &  is a calibrated strain rate coefficient, or

is chosen based on comparison of the salt beingdrilled to “other salts” if possible. It represents the

salt creep rate at 20°C; for dry salt that creeps

slowly, oε &  ≈ 0.002 yr -1

, for a salt that creeps rapidly

(e.g. with carnallite around the salt crystals or with

unusually high moisture content), o&  ≈ 0.02 yr -1.

If vo  can be determined independently [8], o&   for

that particular salt can be calculated. Suppose one

is drilling with an OBM with no salt dissolution,

and that p b is constant. The drill string is withdrawn

with acoustic (ultrasonic) logging of hole diameter,

or a caliper log is lowered to measure diameter(over time if desired). These data give borehole

closure versus time, which is used to determine oε &  

directly. In practice, monitoring trip conditions can

also be used (Fig. 3). If there are zones with otherhalide minerals, it is unlikely that good closure rate

data can be collected because of continued

dissolution of these materials during drilling, even if

OBM is used (the aqueous phase of the OBM may

 be saturated with NaCl, and this means that as other

minerals are encountered, they can be dissolved into

the aqueous phase, reducing apparent closure rate).

ln(εss).

1/T

-Q/R

-Q/R

 (   σ -  p  b

  ) 1,   >  (   σ

 -  p  b  )  2

  (   σ - p

 b   ) 2

ln(εss).

ln(εss).

1/T

-Q/R

-Q/R-Q/R

 (   σ -  p  b

  ) 1,   >  (   σ

 -  p  b  )  2

  (   σ - p

 b   ) 2

 

0.0001

0.001

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

-1

-2

-3

-4

-5

-6

-7

-8

1,000

100

10

1

0.1

0.01

600 8004002000-200

Coble

Creep

Nabarro

-Herring

Creep

HT Dislocation

Climb Creep

Dislocation Glide Creep

FluidAssisted

Diffusional

Creep -

FADC

LT Dislocation

Climb Creep

Homologous Temperature

                                                                                                                                                                                                                                                                                                                                               L                                                                                                                                                                                                                                                       o     

                                                                                                                                                                                                                                                       g                                                                                                                                                                                                                                                                                                                                                                                                                                                      (                                                                                                                                                                                                                                                                                                                                                                       σ        

                                                                                                                                                                                                                                                                                                                                                                                                                   /                                                                                                                                                                                                                                                                           µ                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 )                                                                                                  

Temperature (oC)

                                                                                                                                                                                                                                                                   σ        

                                                                                                                                                                                                                                                                                                                                                                                                                  (                                                                                                                                                                                                                                                                                                                                                                                                                                                                             M                                                                                                                                                                                                                                                                                                                                               P

                                                                                                                                                                                                                                                       a                                                                                                                                                                                                                                                                                                                                                          )                                                                                                  

0.0001

0.001

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

-1

-2

-3

-4

-5

-6

-7

-8

1,000

100

10

1

0.1

0.01

600 8004002000-200 600 8004002000-200

Coble

Creep

Nabarro

-Herring

Creep

HT Dislocation

Climb Creep

Dislocation Glide Creep

FluidAssisted

Diffusional

Creep -

FADC

LT Dislocation

Climb Creep

Homologous Temperature

                                                                                                                                                                                                                                                                                                                                               L                                                                                                                                                                                                                                                       o     

                                                                                                                                                                                                                                                       g                                                                                                                                                                                                                                                                                                                                                                                                                                                      (                                                                                                                                                                                                                                                                                                                                                                       σ        

                                                                                                                                                                                                                                                                                                                                                                                                                   /                                                                                                                                                                                                                                                                           µ                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 )                                                                                                  

Temperature (oC)

                                                                                                                                                                                                                                                                   σ        

                                                                                                                                                                                                                                                                                                                                                                                                                  (                                                                                                                                                                                                                                                                                                                                                                                                                                                                             M                                                                                                                                                                                                                                                                                                                                               P

                                                                                                                                                                                                                                                       a                                                                                                                                                                                                                                                                                                                                                          )                                                                                                  

Deleted: 4

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4.2. 

The effect of temperature

Salt has a high thermal conductivity coefficient (κ)

and can dissipate T differences much more rapidly

than shales and limestones. For example, at 20°Cand 100°C, thermal conductivities of 5.6 and 4.2

Wm-1K -1  have been given. A κ  range for salt istherefore 6 and 4 Wm-1K -1, about 2 to 3 times

higher than κ for shale, limestone, and sandstone.

It is necessary to account for T effects in long salt

sections (e.g. 2000 vertical m), as ∆T can be as high

as 45-70°C between the salt top and bottom. Teffects are accounted for in model simulations by

replacing the salt material property oε & with T ε & :

 

  

  

  

 +

⋅= T  R

Q

oT  e273

1

298

1

ε ε    &&   (3)

Here, the product r· oε &  plays the same role as A in

Eq. 1 and allows an empirical temperature effect

estimate.  Depending on Q, the creep rate increases

on the order of a factor of two for every 16-18°C.

However, reality is not so simple: depending onvarious factors, such as hole size, circulation rate,

riser heat loss, and so on, the mud temperature may be higher or lower than the salt in situ, and this

leads to a non-uniform T(r,t) in the borehole wall.

Though T(r) is easy to calculate if ∆T is constant,

this is rarely the case, and a numerical solution is

used to determine T(r,t). Because of the non-

linearity in Eq. (1), a correct creep calculation now

requires a numerical radial closure calculation.Fortunately, the error arising from an assumption of

a uniform temperature seems to be modest,

compared to the uncertainty in material parameters.

This suggests that the method outlined is

sufficiently robust for practical application.

A critical part of drilling is setting of casing.

Depending on depth, there may be a 10-16 hour

 period between stopping circulation and setting

casing. During this period the hole bottom must not

close excessively so that casing cannot be installed.

Calculations for the lowest salt point is a criticalone in the process of active borehole planning.

Fig. 7  shows a schematic T vs. Z curve for the

drilling fluid in the case on an onshore drilling

operation. In the upper part of the salt interval, thesalt is heated; in the lower part, it is cooled

substantially with respect to in situ T. This has the

interesting effect of reducing the difference in holeclosure rate with depth as a function of temperature:

heating of the salt at the shoe increases the closure

rate at that point, significant cooling at the bit

reduces the closure rate at depth. Hence, drilling

ahead rapidly helps to reduce total creep closure at

the base of the salt interval. There is also the effect

of σθ  redistribution from T-effects: cooling causes

salt shrinkage around the borehole;,this reduces (σ1 

 – σ3)max, and redistributes it farther out into the rock

mass. Reduced σ1 – σ3 means a slower closure rate.

Figure 7: T vs. Z for a Typical Onshore Circulating Well

Figure 8: T vs. Z for an Offshore Deep Water Case

depth

T

casing

geothermaltemperature

bitcooling

heating

mudtemperature

shoe

+T

-T

muddownpipe

coolingin tanks

depth

T

casing

geothermaltemperature

bitcooling

heating

mudtemperature

shoe

+T

-T

muddownpipe

coolingin tanks

0 80

2

3

4

5

1

0

20 40 60

sea

(GoM)

soft

strata

salt strata

sequence

sub-salt

strata

T - ºC

   D  e  p   t   h  -   k  m

geothermal

gradient

T - mud

0 80

2

3

4

5

1

0

20 40 60

sea

(GoM)

soft

strata

salt strata

sequence

sub-salt

strata

T - ºC

   D  e  p   t   h  -   k  m

geothermal

gradient

T - mud

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 A quantitative diagram of T(z) in the drilling fluid

(Fig. 8 is an example for a deep offshore case) can

 be generated by commercial software, giving a

reasonable estimate of the ∆T between the borehole

fluid and the virgin rock. Including all T diffusion

effects into creep analysis makes it necessary to

adopt a numerical model to predict closure, entirelyfeasible, but likely unnecessary in practical cases.

All the required elements for design and hole

 planning in salt have been defined. It is necessary

to have knowledge of the stresses and temperaturesat various depths, and also information about

fracture pressures in non-salt rocks, whetheroverpressures are expected beneath salt, and so on.

These are normal parameters that are collected as

 part of any drilling program.

5.  DESIGN STRATEGY

In drilling thick salt sections, MW and T issues

related to creep closure can be quantifiedreasonably well in advance, and a program chosen

to reduce closure problems.

Figure 9: A Closure Chart with T and Underbalance Effects 

Charts can be generated with creep laws and radial

closure models: Fig. 9 is an example with both

variables of underbalance and T included. Closureis expressed as percent per day, for a given creep

law (different choice of A or T ε & ). In this case, a

“rapidly creeping salt” was assumed. For running

of casing (12 hour time lag), 1% closure is

acceptable, and because the depth gives the ambientT, a mud weight can be chosen to give a value of

closure commensurate with perceptions of risk and

uncertainty. Also, one may study the rate of Tdiffusion into the borehole, using either a simple

axi-symmetric diffusion model, or if desired, a

numerical model may be used (at any depth above

the bit in Figs 7, 8, T = ƒ(z,t)). A T(r,t) example for

a circular borehole is given in Figure 10.

Figure 10: T(r,t) for a Salt at ∆T = 32°C

Consider a sequence such as that shown in Figure 2.

The salt at the base is much warmer than the salt at

the top, and a creep-rate difference of ×6 is a

reasonable expectation. Therefore, it becomes more

important to keep σv – p b smaller at the base to keep

the hole open. How small this should be depends

on the time the hole is open, the diameter of thecasing to be run with respect to the drillhole

diameter, and other factors. Because the lowest

salt is the last drilled, MW can be adjusted to the

desired level for the out-trip before running casing.

In this case, for safety, it may be most appropriate

to assume a “rapidly creeping” salt, and use a low

σv – p b value by increasing MW. Upper salt strata

can sustain some “overbalance” (p b > σv) because

any hydrofracturing tendency in salt is counteracted

 by its impermeable nature and the limited extent to

which a fracture would grow. Upper salt is also

usually heated, so there is tendency to a higher

tangential stress.With a creep model linked to underbalance and

temperature, one can design salt drilling activities

quantitatively and study scenarios equating risks

and costs with factors such as borehole closure rateand ROP. Models are calibrated to reality,

extrapolated to other cases and “windows” of

acceptable closure rates and underbalance defined

in terms of acceptable risk, with charts for specific

areas to define MW ranges for different depths, Tgradients, and so on. These charts are refined

quantitatively as real data become available from

salt drilling.

0 0.25 0.5 0.75 1

40

80

70

60

50

borehole radius

∆T

T - ºC

Radius - m

t = 0 hr 

0.5 hr 1 hr 

2 hr 10 hr 

0 0.25 0.5 0.75 1

40

80

70

60

50

borehole radius

∆T

T - ºC

Radius - m

t = 0 hr 

0.5 hr 1 hr 

2 hr 10 hr 

  1000

10

0.1

0.001

10 201550

 4 0 º C

 7 0 º C

 1 0 0 º C

 1 3 0 º C

σv – pb - MPa

   C   l  o  s  u  r  e   (   %   /   d   )1000

10

0.1

0.001

10 201550

1000

10

0.1

0.001

10 201550

 4 0 º C

 7 0 º C

 1 0 0 º C

 1 3 0 º C

σv – pb - MPa

   C   l  o  s  u  r  e   (   %   /   d   )

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6.  STRATEGIES IN SALT DRILLING

Because salt is impermeable and geochemicallyinert (except for its high solubility), no chemical

means can be taken to improve hole stability: only

stress and temperature can have any effect.

6.1.   Pressures and StressesPressures must be compared to stresses to assess

uphole fracture potential, but in salt, it is possible to

drill overbalanced at the shoe, if it is intact salt with

a thick salt sequence above the shoe (>150 m). This

is because salt has some tensile strength that is more“reliable” than other rocks because it is unfractured,

 because salt at the shoe is being heated by the

warmer mud arising from depth (hence σθ  is

increased), and because fractures will tend to be oflimited length and aperture.  At the shoe, an

overbalance of no more than 5 MPa is advised, andin general, less than 3 MPa is preferred; great care

should in all cases be exercised when p b > σv at thesalt shoe.

6.2. 

 Penetration Rates

Because salt has no porosity or pore pressure, ROP

is less sensitive to degree of balance (σv – p b) than

 permeable rocks (shales, sandstones…). A PDC bitdesigned for salt, which has a low UCS compared to

limestones, anhydrites and low-φ  sandstones, may

encounter problems in cases where salt alternates

with stronger, stiffer rocks. Also, extremely rapid penetration rates lead to severe bit wandering in

salt, but these problems are easy to rectify. In fact,

a high ROP helps reduce salt closure issues.

However, frequent anhydrite or dolomite layers do

not always allow high ROP..

6.3.   Drilling Fluid Type

Mud system choice must address two issues - the

chemical composition of the water phase and the

choice of OBM versus WBM.With respect to water phase chemical composition,

multiple choices are possible but all are guided by

mineralogy. A general rule is to saturate the water

 phase with the most soluble salt(s) to beencountered (except if they are only present in thin

streaks). Thus, NaCl is usually used in the GoM,

Williston and Permian Basins, whereas KCl-MgCl2 

is used in the North Sea Zechstein wells because of

thick bands of bischofite and carnallite. Failing to

follow this strategy may lead to serious problems of

mud contamination, flocculation and difficulty inadvancing. To continue drilling, the mud system 

has to be changed, and in the interim delays, often

including density maintenance problems, hole

closure is large enough to require full section

reaming or a sidetrack. 

Should one use WBM or OBM? Using salt

saturated WBM with sheared attapulgite for

viscosity had already showed its limitations as early

as the 1970’s. A salt-saturated WBM at surface

conditions is not saturated at downhole conditions,leading to washouts, often beyond mechanical

caliper limits. Cementing then becomes extremelydifficult, and the irregular cementation leads to

irregular casing loading and consequent early casing

collapse (many examples around the world have

 been well documented).

To avoid this, WBM must be “oversaturated” at

surface conditions. One claimed way of doing this

is to use chemical additives to increase salt (NaCl)

solubility under surface conditions. However, field

testing of this technique has shown mixed results.

In some cases, caliper data showed better profiles –i.e. less enlargement – in other cases it did not.

Furthermore, laboratory dissolution tests have

shown that few commercially available chemicals

had any significant benefit. Also, this approach was

not appropriate for other salt saturated muds such asthe KCl-MgCl2 systems used in the North Sea.

Another WBM technique has been developed by

 North Sea operators: the mud is heated on surfacethrough the use of a heat exchanger so that surface

temperature becomes equal to downhole circulating

temperature. (The hot fluid source is generally

 produced hydrocarbon on the same platform.) By

salt saturating the hot mud, less downhole

dissolution occurs, and the method has proved

highly successful and is favored by several

operators involved in sub-Zechstein plays in the

southern North Sea.

Using OBM with an appropriate water phase

salinity will strongly reduce if not suppress

dissolution. As a consequence, salt closure may become a more important issue because there is no

dissolution to counteract it; this can lead to serioustripping difficulties. For example, in Williston

Basin deep drilling operators are known to short trip

the hole every stand to fight against salt closure,

hence losing extensive amounts of drilling time.

In OBM, an obvious method is to use as high a mud

weight as possible to minimize σv – p b. However,

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salt horizons are often surrounded by thief zones –

fractured formations where losses are frequent.

Using a high mud weight is not feasible everywhere

and particularly not where several salt zones have to

 be drilled in one section, with intervening zoneswhere losses can occur.

The second method to fight salt closure is to use bi-

centered bits and under-reamers close behind the bit

to enlarge the hole and gain time; this technique has been tried in practice with various degrees of

success. Its main downside is that under-reamersand bi-center bits do not react well when hitting

repeated hard anhydrite and dolomite streaks.

The third method to minimize closure is to cool the

mud and use the temperature sensitivity of salt

creep, which can be quantified using analysis.

Thus, a choice is to be made between OBM and

WBM. OBM has minimal ability to dissolve salt,even other halides encountered in thin beds. OBM

is favored for drilling the upper hole where drillinggoes from ductile shales and mudstones into salt.

Where lost circulation is common above salt, WBM

is cheaper. In continuous salt sections, NaCl-

saturated WBM is favored.

In theory, salt dissolution using a slightly undersatu-

rated aqueous base drilling fluid is an option to cope

with creep closure; in fact, this is achieved naturallyin the drilling process from the changing

temperatures with depth and precipitation of salt inthe surface mud tanks. Furthermore, because the

hole bottom is the zone of the largest underbalance

and therefore highest closure rate, the salt is

 preferentially removed from the most appropriate

region. In fact, however, most of the resaturation ofthe drilling fluid takes place from dissolving salt

from the drill cuttings rather than from the borehole

wall, and this controlled dissolution strategy isdifficult to use in a quantitative manner, and is in

general not advised, unless the salt section can be

drilled rapidly in just a few days, so as not to lead to

washouts.

6.4.   Drilling Other HalidesIf OBM is being used, when a seam of a mineral

such as bischofite or carnallite is encountered, the

saline aqueous phase of the OBM (~40% by

volume) is unsaturated with respect to the new

mineral. Because the aqueous phase was NaClsaturated, there will be a slow dissolving of the new

minerals, precipitation of NaCl in the mud (the

common ion effect) and gradual hole enlargement

will tend to occur in the region of the new minerals.

However, there is little direct contact between the

aqueous phase globules and therefore the

dissolution rate is slow.

If the creep rate of the non-salt halide bed is higher

than that of NaCl at that [T, σ]-state, the higher

dissolution rate focused in the new mineral zone

tends to over-compensate for this behavior, and this

leads to fewer borehole closure problems.

6.5.  Cooling the Mud

Clearly, because of the T-sensitivity of salt creep, itis a viable strategy to cool the mud deliberately [9].

Offshore, this may happen automatically because of

heat transfer through the riser (Fig 8). This means

the mud going back down the hole is thoroughlychilled (although the use of seafloor booster pumps

changes matters). Onshore, the cooling effect of theriser is lost and mud may come out of the hole at

70-80°C (as in Kazakhstan salt drilling). In thesecases, there is merit in considering cooling the mud

through heat exchange (a problem in desert areas,

 but not in the shallow Caspian Sea conditions for

the Kashagan oil field).

In the case of setting casing in a rapidly closing salt,it is possible to circulate cooled mud for 10-15

hours before tripping to run casing, taking

advantage of the reduced creep rates and the more

favorable stress conditions around the wellbore. Asa rule, circulate with the coolest mud possible

without rotation, and circulate 1.5 hours for each

hour that the hole will be in a static condition.

6.6.   Exiting SaltA critical period in drilling is when salt is being

exited, either at the base of a thick salt section (Fig

1c) or from the flank of a salt dome (Fig 1b). If a

zone of pressure reversion and stress reversion

exists below the salt, sudden lost circulation cantake place. If there is trapped overpressure, high po 

can be encountered. In many locations a rubblezone with salt-occluded porosity (hence low k)

exists, and a good strategy in these cases is to place

a strong casing with the shoe below the base of the

continuous salt beds, reducing all types of well

control risks. The salt blocking the pores helps in

keeping troubles at bay while completing the well.

If the sediments below the salt are not salt blockedand stresses or pressures are abnormal, great care

must be exercised in locating the subsalt shoe just atthe exit point, or somewhat above it (though this

 point is hard to determine in practice). In such

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cases, loading mud with LCM just before exiting

the salt is a strategy to maintain hole control [11].

In the case of salt domes, exiting through the flank

means exiting into a shear zone where the country

rock may be fractured, sheared, and so on. Also,

the thickness of the sediments that may be salt

cemented is often less than in the case of bedded

salt, giving less room for error.

6.7. 

Cementing Through Salt

Salt will dewater cement through osmotic suction,

generating an annular zone of free water eventhough the cement achieved full displacement. This

is not a serious issue in pure salt because continuedclosure will eventually expel the brine, giving

uniform loading, but in the case of sedimentary

rocks (matrix-supported) with salt in the pores, a

gap between cement and the rock can be generated.

A good solution to potential salt problems is to use

denser cement. A carefully graded quartz filler

material with a wide grain size range is used, with

D50 ranging from 20 µm (silt) to 500 µm (coarse-grained sand). Type-G cement content is reduced,

and a superplasticizer agent is added to sustain

 pumpability. This allows placement of cement thatis far less prone to shrinkage than conventional

cement, and far stronger as well, so that when it

sets, it tends to generate a stronger overall structure.

Casing problems in salt are usually associated with

differential or irregular displacements at interfaces

 between salt and an insoluble rock, or with awashed out zone [12]. Creep of salt means that

 point loads can be generated, and this is the most

dangerous condition for casing impairment. To

cope with this, it is possible to design a casing

string so that a special schedule casing is used

across the zone of concern, so that point loads can

 be more easily accommodated without a buckling ofthe casing. Also, the more uniform the cement

sheath and the stronger it is, the more likely the

wellbore will withstand a point load arising from

differential closure. The same cannot be said for a

generalized shear displacement if such a

displacement is being load activated by large-scale

and distant loads [10].

7.  CONCLUSIONS, RECOMMENDATIONS

Drilling salt can be accomplished safely by

applying knowledge of stresses and material

 behavior through simple models that capture the

critical aspects of borehole processes such as creep,

heat flux, temperature sensitivity, and so on.

Recommendations for drilling salt follow:

1.  Carry out a careful estimate of T and σv before

drilling so that underbalance level and hole

closure rates can be quickly calculated. Because

of viscous behavior, assume that stresses in salt

are isotropic and = σv.

2.  In drilling into thick salt bodies (thick tongues,

 beds or domes), place the salt casing shoe asdeeply into the top part of the salt bed as

 possible to avoid an extra casing string. This is

 particularly important offshore.

3.  Drill long salt sections with a PDC bit as rapidly

as possible, as time is of the essence in drilling

through creeping materials. Vibration manage-

ment devices may help when non-salt intervals

and xenoliths in the salt strata are drilled.

4.  Carry out an assessment of the creep closurerate likely to be encountered in the worst

conditions. Because of uncertainty, a range of

4-5%/d closure rate seems appropriate as a

maximum rate criterion.

5.  In all cases, drilling mud density can be adjusted

to reduce closure rates, but limits exist because

of potential fracture problems at the shoe in salt.

However, the consequences of such fracture are

less serious than in porous strata.

6.  Drill with a fluid density sufficient to keep creepclosure below 4-5%/d in the most rapidly

creeping section, which will usually be at the

 base of the hole where the salt is hottest and the

underbalance (σv – p b) is the greatest.

7.  Either OBM or WBM may be used;  in both

cases the aqueous phase is best kept saturated. 

It seems of little use to “design” undersaturated

WBM to counteract closure, and additive use toaffect salt dissolution rates is of little value.

8.  If other non-NaCl halides will be encountered in

drilling and these minerals have a higher creep

 potential than salt, installing back reamers at thetop of the BHA is advised in case of rapid

 borehole closure leading to BHA sticking.

9.  In rapid drilling of long salt sections, the use of

an under-reamer and stabilizer above a steerablerotary bit assembly can help achieve high rates

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without excessive deviation. This requires

MWD technology and trajectory corrections.

10. Collection of closure data with acoustic calipers

on trips will help in the calibration of creep

models, which in turn will help guide

subsequent holes in the same salt section.

11. Because salt creep rate is T-sensitive, closure

rate can be reduced through cooling the drilling

fluid. Cooling can be used just before casing

setting so that the hole may be left for 10-15

hours without excessive closure.

12. In drilling through a thick salts to exit at depth,

set casing a few metres after exiting salt so that

the shoe is in matrix-supported sediments where

 permeability may be blocked by salt,

minimizing hydraulic facturing or blowouts risk.

13. Casing distress in salt sequences is related to

 poor hole profiles or interfaces between salt and

other rocks, leading to point loads on the casing

 because of closure. There is merit in using high

density cements (minimum of cement powder,graded inert filler of sand and silica flour).

Also, a strong cement sheath and steel casing

helps counteract creep tendencies; expandableliners and casings may have few applications in

salt.

8.  SYMBOLOGY

A, a empirical or measured coefficients

E Young’s modulus (i.e. “stiffness)

FADC Fluid-Assisted Diffusional Creep

MW drilling fluid unit weight (mud weight)

n exponent on stress in a creep law

 p b  borehole pressure, generally mud pressure

R Universal Gas Constant

ROP Rate Of Penetration (in drilling - m/hr)

Q activation energy for a specific process

T temperature (°C or °K)

t time, z depth

γ     bulk density, γ   : mean bulk density

ε &   strain rate (steady state with subscript “ss”)

 sε & T &   material constants for strain rate

η   viscosity (e.g. of a rheological element)

κ   thermal conductivity

σ  stress (subscripts 1,2,3 for major,

intermediate and minor stresses)

σ1 - σ3  plastic stress (deviatoric stress)

σo  a normalizing stress value

σv, σhmin, σHMAX, principal earth stresses

REFERENCES

[1] Dusseault, M.B., V. Maury, F. Sanfilippo and F.-J.

Santarelli. 2004. Drilling around and under salt: Stressesand uncertainties. Proc. North Am. Rock Mech. Symp,GulfRocks 2004, these proceedings.

[2] Fredrich, J. T. and A.F. Fossum. 2000. Large-scale three-dimensional modeling of reservoirs: Examples fromCalifornia and the deepwater Gulf of Mexico. Oil & Gas

Science and Technology – Rev. IFP, 57 (5), 423-441.

[3] Rothenburg, L. Dusseault, M.B. & Mraz, D.Z. 1999.

Steady-state creep of salt in mines follows a power-lawexponent of 3.0, based on a reanalysis of published dataand mine simulation. Mecasalt 99, Bucharest, Romania.

[4] Frayne, M.A. and Mraz, D.Z. 1991. Calibration of anumerical model for different potash ores. Proc. 7th  Int

Congress on Rock Mechanics (Aachen), Balkema,Rotterdam,471-475

[5] Rothenburg, L. 1999. Personal communication andunpublished analyses, Univ. of Waterloo, Waterloo, ON

[6] Dusseault, M.B., Mraz, D., Unrau, J. & Fordham, C.J.1985. Test procedures for salt rock. 26th US Symp onRock Mech. (ed: E. Ashworth), Balkema Rotterdam, 313-

319.

[7] Bogobowicz, A., Rothenburg, L. & Dusseault, M.B. 1991.

Solutions for non-newtonian flow into elliptical openings,Jour. of Applied Mechanics, ASME, V. 58, No. 3.

[8] Preece, D.S. and Goin, K.L. 1986. Experimental andtheoretical studies of salt creep closure of the SPR Big Hill

site, Wells 106 – 110. Sandia Nat’l Laboratories,Geotechnical Div Rept SAND86-0191

[9] Maury V. and Guenot A. 1995. Practical advantages ofmud cooling systems for drilling. SPE Drilling and

Completion March, pp 42-48 SPE#25732.

[10] Dusseault, M.B., Bruno, M.S. & Barrera, J., 2001. Casingshear: causes, cases, cures. SPE Drilling & CompletionJournal Vol.16 Num. 2, 98-107.

[11] Whitfill, D., Rachal, G., Lawson, J. and Armagost, K.2002. Drilling salt – effect of drilling fluid on penetrationrate and hole size. SPE/IADC Drlg. Conf., Dallas, #74546

[12] Willson, S.M., Fossum, A.F. and Fredrich, J.T. 2003.Assessment of salt loading on well casings. SPE J. ofDrlg. and Completions, March, pp 13-21.