01fundamentals of Frac

8/19/2019 01fundamentals of Frac

1/15

1 Material Balance

Fundamentalsof Fracturing Engineering

Material Balance


2/15

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…)


3/15

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


4/15

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


5/15

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


6/15

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


7/15

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


8/15

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


9/15

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 ?


10/15

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

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01fundamentals of Frac