01fundamentals of Frac
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Transcript of 01fundamentals of Frac
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8/19/2019 01fundamentals of Frac
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1 Material Balance
Fundamentalsof Fracturing Engineering
Material Balance
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2 Material Balance
Data Collection
Uncontrollable parameters1. K, h & ΦΦΦΦ
2. σand their orientation
3. Formation temperature4. Reservoir pressure
5. Type of Reservoir fluid
6. Rock Properties
Controllable parameters1. Casing, Tubing, & Completion
configuration
2. Downhole equipment
3. Perforation ID and Length & SPF &Phasing
4. Fracture treatment (Rate, PropConcentration, Fluid, Proppant, etc…)
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3 Material Balance
Controlling Parameters: Stresses
Tectonic
StrainElastic
Modulus
Tectonic stresscomponent
Lithostatic stress model
Poison’s
ratio
Pore Pressure
Over
hydrostatic
Virgin
Slight
depletion
Shale static
Depleted
Stress Contrast forFrac Model
Closure Pressure
calibration through:
Microfrac, DataFRAC
+ =
Lithology
gas
Overburden
σLit = ( ν /1- ν)*(σΟΒ - αpr) + α pr
oil
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4 Material Balance
Rock Mechanic
PropertiesReservoir
Properties
Properties Affecting Frac Geometry
Hydraulic geometry (Dynamic)
h
Lw max
Propped geometry
x f w f
h o
C L
E
C L
∆σ ∆σ ∆σ ∆σ
〈w〉
E
pc
σ σσ σ min
c f
Fracture Properties
kh/µpr
ΦctcR
σ σσ σ OB
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5 Material Balance
Fracture Engineering fundamentals
Basis for frac modeling and analysis
• Volume balance : V in = V frac + V loss• Elasticity : width -vs- pressure ( E)
• Elasticity : containment –vs- height growth
• Frictional fluid flow : frac fluid pressure drop inside the fractureAnd a few more: proppant transport …..
Analysis and evaluation :
based on pressure response after a constant rate injection
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6 Material Balance
Volume balance
based on volumes: Vin= Vfrac+ Vlost
Vfrac = Af (area) * wh (width)
Vlost from G function go ,leakoff CL , Spurt Sp
Know hf then how do we get L? ….
Qi ti = Af ( wh + 2 vL )
Af = Qi ti / ( wh+ 2 vL )
L = Af / 2 hf
vL~ go CL √ti + Sp , go ~1.5
2 L
Af = (2 L) hf hf
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7 Material Balance
Elasticity 1: width ~ Pnet
Relation between Pressure and width
• need modulus E And height hf
• need βL the ratio of average width over the frac length to wmax at the well:
• Introduce definition of compliance cf =π βL hf / 2E
Provides the average frac width wh for given Pnet…
pf
wh
pc
cf ~ hf / E
pnet = pf - pc = (E / 2 hf ) wmax (PKN)or wmax = (2 hf / E) pnet (wellbore)
wh is A= (π/4)h βL wmax ~ 0.55 wmax
wh=(π βL hf /2E) pnet=(cf ) pnet
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8 Material Balance
The β ratio = average / wellbore values
There is a gradient of pressure along the fracture, therefore need ratio for
calculating “length-averaged” values in terms of p at the wellbore
β =pnet
pnet,w
=pf - pcpw - pc
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9 Material Balance
Material Balance: governs “placement” and cost
How much fluid to get L ?
Af
= Qi
ti
/ (wh
+ 3 CL
√ ti
), L= Af
/ 2 hf
→ fluid cost
pnet = pf - pc = E wmax / 2 hf Psp*Q → HHP
How much prop can we put ? prop width/ hydraulic with
wp = Vp / Ap = Vp / (2 Lp hp ); wp / < wh> = cf / (1-φ) → Prop cost
wp / wh ~ 1/6 (3 ppa) and 1/2 (10 ppa)
How many pump we need ?
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10 Material Balance
Elasticity 2: height growth,∆σ∆σ∆σ∆σ and ∆∆∆∆h/ho
Relation between initial height ho and hf total frac heightInsight from ideal equal barrier
Barrier depends on : (1)∆σ∆σ∆σ∆σ (2) thickness /initial height ∆∆∆∆h/ho
1.0
2.0
3.0
4.0
5.0
0.3 0.4 0.5 0.6 0.7 0.8 0.9
pnet / ∆∆∆∆σσσσ
h
/ h o : i d e a l 3
- l a y e r
0.0
0.5
1.0
1.5
2.0
∆ ∆∆ ∆ h
/ h o : ~
g e n e r a l 3 - l a y e r
∆∆∆∆ h ~
ho/10
2x
hf ~ ho . f ( pnet / ∆σ)
∆σ∆h
hf ho
pnet
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11 Material Balance
Coupling elasticity – fluid frictional dropPnet at the wellbore = Frac fluid frictional flow ( pressure drop in the frac )
pnet(elasticity) = ∆∆∆∆p(frictional drop)
Frictional flow from 1D (linear ) Darcy with x-section area =height .width , hf wh
equate
solve for average width wh
Rate or viscosity double (µµµµa Qi ): effect on wh & pnet? (21/4 = 1.2)
Qi = k (hf wh )/ µa ∆p/L ; with k ~ w 2
rearrange
∆p/L = µa [Qi /(hf wh )] / wh2
wh ~ (µa Qi L / E )1/4, pnet = (E / 2 hf ) wh
pnet / L ~ E wh / hf L = ∆p/L = µa [ Qi / (hf wh )] / wh2
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12 Material Balance
Width equation for Power law
Use more complex but actual power law frac fluid
µµµµa,PL =τ ττ τ //// γ γγ γ = K/ γ γγ γ 1- n; γ γγ γ ~ Q/hw2
Even less dependent on rate
( )
2,9.0,2
8.0,2
;)(
5.0~;3~223
1
,2
→→→
→→
∝
≈= +=
p net
net
max
max max net
t pQ
Q
p
Q Lw
n n
/ n
hQ
E h L K ww p e
e
h E
µ µ
µ
µ
0.170.33
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13 Material Balance
Frac design for L quadratic equation of √ti
Summary• Mass balance : Vin= Vfrac+ Vlost Af = Qi ti / ( wh+ 2 vL), L= Af / 2 hf • Elasticity (width) : pnet = pf - pc = E wmax / 2 hf = (1/cf ) wh
• Elasticity (Height) : hf ~ ho . f ( pnet / ∆∆∆∆σσσσ)• Frictional drop : wh ~ ( µµµµa Qi L / E )1/4
All information to solve
The design solution : quadratic equation of √ti for any given L !
Get ti
, wh ,
Vfrac
, efficiency η ηη η and pnet
= (1/cf
) wh
= (2E /hf
ππππ ββββL
) wh
Note : to get L for a given ti an iterative convergence is required
Af = (2 hf L) = Qi ti
/ [ wh+ 2 (1.5 CL √ti + Sp ) ]
Basic input: Qi , L, CL , Sp, µa , E , ho , ∆σ
Qi ti - (2 hf L) [ wh+ 2 (1.5 CL √ti + Sp ) ] = 0
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14 Material Balance
Key Role of Efficiency: proppant scheduling no TSO
fluid efficiency: ηηηη = Vfrac / Vin < 1; cin = ηηηη cfrac
Vici
VL
Vfcf
frac
∞∞∞∞→→→→ Lu
x / L
V / VEOJ
1
pad
x / L
segment or total
cD
pad
f p ≅1+ η
1- η
V / VEOJ
η
segment or total
u L leakoff velocity ft/min goes to infinity at tip
ττττ
SPE 13278 Determination of Proppant and Fluid Schedules From Fracturing-Pressure Decline (Nolte 1986)
cD =cin/cf,EOJ
0 1
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15 Material Balance
proppant scheduling with TSO
Base on relation for no TSObut noting
• Vin → Vin,so
• ηηηη → ηηηηso
after TSO no loss at tip
ηηηηEOJ >>>> ηηηηsoand
cin/cf,EOJ
pad
f p ≅1+ η
1- η
V / VEOJ
η
cin/cf,EOJ
pad
f p,so ≅≅≅≅1+ ηηηηso
1- ηηηηso
V in,so/ VEOJ
ηsof p,EOJ = f p,tsoVin,t
soVin,EOJ
ηEOJ