Modeling of fluid transport and storage in organic-rich shale
Shale Fluid Interaction
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Transcript of Shale Fluid Interaction
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Shale/Fluid Interactions
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Introduction
Shale instability is a costly problemfor the oil and gas industry Shale makes up over 75% of drilled
formations
Shales cause over 90% of wellbore instabilityproblems
Wellbore instability problems cost the oil
industry >> $1billion/year
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Wellbore Instability Problems
Shrunk Hole
LostCirculation
Overgauged
HoleGauged Hole
Brittle Shale
Swelling Shale
Friable Sandstone
Tensile Failure
(Breakdown)
Compressive Failure(Collapse)
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Mechanisms of Wellbore Failure
Increase in pore pressure and decrease in
effective stresses
Shales can act as leaky semi-permeable
membranes that generate an osmotic
pressure
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Transient
water and solute flux
Transient flow
Time dependent wellbore failure
Failure away from wellbore wall
Thermal effects (fully coupled)
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Use of Non-Aqueous Drilling Fluids
Advantages
Can prevent problems caused by fluid/shaleinteractions
drill-string balling
borehole instability.
Can provide excellent filtration control, lubricity andstability at high temperatures.
Disadvantages
Can result in excessive loss of mud because of lowfracture extension pressures.
Are subject to stringent environmental regulations, andcan result in costly liabilities.
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Differential Pressure
The difference between the boreholepressure and the formation pore
pressure is a driving force affectingtransfer of fluid from drilling mud toshale formations.
Increasing mud density can raise thedifferential pressure and contribute toshale hydration.
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Osmotic Potential
Chemical Potential is a driving force determined
by the relative water activities of the drilling mud
and the shale pore fluid at downhole conditions.
The chemical osmotic force and resulting transfer
of fluid is dependent upon the efficiency of the
leaky-semipermeable membrane
Hydraulic potential will compete with osmotic
potential in affecting the shale swelling.
Manipulating the concentration of drilling fluid
can control shale swelling
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Diffusion
Diffusion osmosis is determined by the differences in theconcentrations of the individual solutes in the drilling mudand in the shale pore fluid. Ions and molecules of eachspecies tend to move from the high to low concentration.
The flow of solute and associated water is dependent
upon the solute selectivity of the drilling mud/shaleinterface at downhole conditions for each individual solute.
When using a water-based mud, diffusion osmosisopposes chemical osmosis. A lightly compacted shale (high permeability shale) having
large pore throats favors diffusion, A more compacted shale favors chemical osmosis.
Higher membrane efficiency and lower permeability
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Drilling Mud / Shale Membrane System
Non-aqueous based muds (diesel, mineral, synthetic)can provide an ideal semipermeable membrane thatprevents diffusion of ions and molecules. Reduce the shale/fluid interactions
Helps to reduce shale instability problems Water-based muds do not provide an ideal semi-
permeable membrane. Leaky membrane
Shale/fluid interactions Diffusion
Hydraulic driven
Osmotic pressure
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Stresses Induced by Pore Pressure and
Formation Temperature Changes
(Yew and Liu [1992], Wang[1992],Chen[2001])
),(
13),(
1
21
),(,1
13
),(,1
1
21
,
1
13
,1
1
21
2
2
2
2
2
2
2
2
trTE
trp
pr
rtrTrdrtrT
r
E
trprdrtrpr
pr
r
rdrtrTr
E
rdrtrpr
fmf
zz
wwf
r
r
fm
f
r
r
f
ww
r
r
fm
r
r
f
rr
w
w
w
w
l M d l F Fl i
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eneral Model For Flow inShales
Transport Model
for Water
and Ions
Continuity Equations
+
Flux Equations
Activityof Water
and
Osmotic
Pressure
Coupling Coefficients
for Shale Kijor Lij
Flux of Water and Ions
Into ShalePressure and Ion
Concentration Profile
Swelling Pressures and
Osmotic Pressure
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Mathematical Model
XPo
Co
wP
dfC
y
x
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Water Activity
Suppose the water activity of the solution is a
function of solute concentration:
aw=f(Cs)
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Osmotic Pressure
For ideal solutions
S
=nRT(CS
-Cdf)
For non-ideal solutions
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Coupled Flux Equations
(De Groot [1958] & Prigogine[1968])
333231
232221
131211
KKPKI
KKPKJ
KKPKJ
s
sD
sv
v
s
sD J
C
JJ
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Continuity Equations
0x
J
t
Css
0 vJxt
oo PPc exp
01
x
J
cx
PJ
t
P vv
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Phenomenological
Coefficients
33
3113
11
K
KK
KKI 33
3213
12
K
KK
KKII
33
312321
L
LLLLI
33
322322
L
LLLLII
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Fully Coupled C-P Equations
0,,,
0,,,00,,,0
..
01
0
00
00
tPPCCx
tPPCCxxPPCCt
CB
x
CnRTKx
PKxct
P
x
CL
C
LnRT
x
PL
xt
C
s
wdfs
s
sIII
sI
s
III
s
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Assumptions & Simplifications
(Ideal Solution)
No chemical reactions
Constant temperature
LI,LII,KI,KIIare constant
1&1
2
x
C
x
P
x
P s
P P M d l
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Pore Pressure Model(Ideal Solution)
)( ijeff KfD
00
00
;,0,
;,0,;,,0
ppCCtr
ppCCtrrppCCrrt
S
wdfSw
Sw
02
t
C
cD
nRTKp
c
K
t
p S
feff
II
f
I
02
Seff
S CDt
C
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Permeability
11
kk
33
3113
11
33
321312
0
k
kkk
kkkk
p
vJ
Reflection Coefficient
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Fluxes
Solute
x
CL
C
LnRT
x
PLJ
Solventx
CnRTKx
PKJ
sI
s
IIIs
sIIIv
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Cdf/Co=0.01M/1M
0.80
0.90
1.00
1.10
1.20
1.30
0 20 40 60 80 100 120
x (mm)
PD
t=3hr
t=12hr
t=24hr
Pressure Profile Variation
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Non-Ideal Case
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Verification in the Case of
Ideally Dilute Solution
)1( SWWWW nxxxa
WSW nnnn
For ideal dilute solution:
(n is the dissociation number)
For dilute solution, it gives:
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W
S
W
S
SW
SS
n
VC
n
n
nnn
nx
W
S
SSW n
nVCnxCfa 11)(
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For nW=1 mole, V is the molar volume of pure water
SSSW nVCnxCfa 11)(
the water activity goes to 1 when CS0
nVCf S )('
nVCf
Cf
S
S )(
)('
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nVCf
Cf
S
S
)(
)('
02
2
2
2
x
C
c
nRTK
x
P
c
K
t
P sIII
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nVCf
Cf
S
S
)(
)('
0
x
CL
C
LnRT
xt
C sI
s
IIs
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Water Activity for NaCl
Solutionsy = -0.0027x 2- 0.0303x + 1
R2= 0.999
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6
C(mol/L)
aw
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Abnormal Pressure
Cdf>Co
-0.4
-0.2
0
0.2
0.4
0.6
0.81
1.2
0 50 100 150 200
x (mm)
Pd
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Abnormal Pore Pressure
500psi
0
0.5
1
1.5
2
2.5
0 200 400 600 800 1000
x(mm)
Pd
Co=3M,
Cdf=0.01M
P P P fil A d
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Pore Pressure Profile AroundWellbore
Time=3hr Time=9hr
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Pressure Profile
Variation with Time (Cdf
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Estimating Model Input Parameters
shaleP1
C1
P2
C2
P1 P2, C1= C2 Pressure buildup KI
P1 P2, C1C2 Pressure buildup KIIRadio active tracer Deff
Experimental Data from Chevron
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Experimental Data from Chevron(R. T. Ewy 2000)
Confining Pressure
Test Fluid (WellborePressure)
Pore PressureGauge
ShaleSample
Screens or porous metalJacket
Confining PressureConfining
Pressure
Summary of Model Parameters and Their
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Summary of Model Parameters and TheirEffects on the Behavior of Pore Pressure
II
0
100
200
300
400
500
600
700
800
900
1000
0 10 20 30 40 50 60
t (hr)
P(
psi)
KI
KII
Deff
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Diffusion Coefficient
D vs CD
y = 3E-10x
2
- 1E-09x + 7E-10R2= 0.9996
0.00E+00
2.00E-10
4.00E-10
6.00E-10
8.00E-10
0 0.2 0.4 0.6 0.8 1CD
D
Pressure Profiles in a Constant Volume Swelling
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Pressure Profiles in a Constant Volume Swelling
TestPh
awdf
awsh
P
PT
P
Ph
PT
awdf aw
df
P
PT
Ph
Time t = 0 Time t =Time t8
PT, average ORPconfining
Time
Ph, average
Paverage
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Shale Properties(R. T. Ewy, 2000)
Shale
Sample
Clay
Contents
CEC(meq/100g)
Surface Area
(m2/g)
Permeability(microdarcies)
A1 20%-25% 5.3, 3.8 23, 25 1~2
A2 50%-75% 14.6, 10.8 227, 230 0.001~0.004
N1 65%-75% 16.5, 16.8 209,212,256,261
0.002~0.008
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Input Data for A2-1-G
Drilling fluid salt concentration 267g/L CaCl2
Pore fluid salt concentration 0.01M
Pressure of drilling fluid 1020 psi
Pore pressure 5 psi
KI 2.344X10-18
m3s/kg
KII -1.394X10-19
m3s/kg
Deff 8.94X10-11m2/s
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Comparison of Model with Data A2-1-G(To obtain parameters)
A2-1-G
0
100
200
300
400
500
600
700
800
900
1000
0 10 20 30 40
t (hr)
PorePressure(psi)
Experimental Data
Model fit
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Input Data for A2-2-A
Drilling fluid salt concentration 413g/L CaCl2
Pore fluid salt concentration 0.01M
Pressure of drilling fluid 955 psi
Pore pressure 50 psi
KI 2.344X10-18
m3s/kg
KII -1.394X10-19
m3s/kg
Deff 8.94X10-11m2/s
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