Fracture Dimensions

Hydraulic FracturingHydraulic FracturingShort Course,Short Course,

Texas A&M UniversityTexas A&M UniversityCollege StationCollege Station

20052005

Fracture Dimensions Fracture Dimensions

Peter P. ValkóPeter P. Valkó

Hydraulic FracturingHydraulic FracturingShort Course,Short Course,

Texas A&M UniversityTexas A&M UniversityCollege StationCollege Station

20052005

Fracture Dimensions Fracture Dimensions

Peter P. ValkóPeter P. Valkó

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Proppant Placement

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Proppant Placement Concepts

From dynamic width (hydraulic) to propped

width (after frac closes on proppant)

Areal proppant concentration

Added proppant concentration

Max added proppant conc

Proppant (placement) efficiency

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Proppant Transport: Settling

Settling causes problems

proppant efficiency decreases (proppant

leaves pay layer)

screenout danger

No settling in “perfect” transport fluid

Viscosity (rheology) and density

difference

(Foams: visc good, dens: bad)

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Design Logics

Height is known (see height map)

Amount of proppant to place is given (from NPV)

Target length is given (see opt frac dimensions)

Fluid leakoff characteristics is known

Rock properties are known

Fluid rheology is known

Injection rate, max proppant concentratrion is given

How much fluid? How long to pump? How to add

proppant?

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Key concept: Width Equation

Fluid flow creates friction

Friction pressure is balanced by injection pressure

Net pressure is positive

Fracture width is determined by net pressure and characteristic dimension (half length or half height)

The combination of fluid mechanics and solid mechanics

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Two approximations:

Perkins-Kern-(Nordgren)

Vertical plane strain

characteristic half-length ( c ) is half height, h/2

elliptic cross section

Kristianovich-Zheltov - (Gertsmaa-deKlerk)

Horizontal plane strain

characteristic half length ( c ) is xf

rectangular vross section

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Width Equations (consistent units)

width: w, wo, wwell,o viscosity: inj. rate (1 wing): qi

half-length: xf

plain-strain modulus: E'height: hf

)x(hw=V fff

Perkins-Kern-Nordgren PKN4/1

0, '27.3

E

xq=w fi

w

0,628.0 www

Kristianovich-ZheltovGeertsma-De-Klerk KGD

4/12

'22.3

f

fiw hE

xq=w

www 785.0

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PKN Power-Law Width Equation

With equivalent viscosity at average shear

rate

the maximum width at the wellbore is

22

11

22

122

2222

1

0, '

14.2198.315.9

n

fn

fn

inn

n

n

n

nw E

xhqK

n

n=w

0,ww Power Law fluidK: Consistency (lbf/ft2)·sn

n: Flow behavior index

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Material balance +Width Equation

Vfe = Vi - Vlost

qi

2qi

A

Vi = qi te

Lost: spurt +leakoff

xf

Averagew(xf)

hf

)x(hw=V fff

A w=Vf

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Pumping time, fluid volume, proppant schedule: Design of frac treatments

Pumping time and fluid volume: Injected = contained in frac + lostlength reached, width created

Proppant schedule: End-of-pumping concentration is uniform, mass is the required

Given: Mass of proppant, target length, frac height, inj rate, rheology, elasticity modulus, leakoff coeff, max-possible-proppant-added-conc

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1 Calculate the wellbore width at the end of pumping from the

PKN (Power Law version)

2 Convert max wellbore width into average width

3 Assume a = 1. 5 and solve the mat balance for inj time,

(selecting sqrt time as the new unknown)

4 Calculate injected volume

5 Calculate fluid efficiency

22

11

22

122

2222

1

0, '

14.2198.315.9

n

fn

fn

inn

n

n

n

nw E

xhqK

n

n=w

0,628.0 we ww

022

)Sw(tκ C t

xh

qpeL

ff

i

eii tqV

i

eff

i

fee V

wxh

V

V=

Pumping time, slurry volume (1 wing)

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Nolte’s power law proppant schedule:

fpad1 V/Vi0

C/C e

1

slurry

y =

0 1

1

1ie VcM

1

11

0

dxx

1

1)1( padfArea

1

1Area

Nolte's proposition:select fpad=

ie VcM

1

1

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1 Calculate the Nolte exponent of the proppant

concentration curve

2 Calculate the pad volume and the time needed to

pump it

3 The required max proppant concentration, ce

should be (mass/slurry-volume)

4 The required proppant concentration

(mass/slurry-volume) curve

5 Convert it to “added proppant mass to volume of

clean fluid” (mass/clean-fluid-volume)

e

e

1

1

ipad VV

epad tt

pade

pade tt

ttcc

iee V

Mc

propp

added cc

c

1

Proppant schedule calculation

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Gross and Net Height

2qi

A

Vi = qi te

Vfe = Vi - Vlost

Lost: spurt +leakoff

rp= hp /hf

hp

2D design: hf is given

hf

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Ex_2: Frac Design

Pay: 45 ft Gross: 67.5 ft (Gross = hf)

Proppant mass (2wing) = 100,000 lbm is available2/3 will go to pay layer

Slurry injection rate (2qi) = 30 bpm Created fracture height is 67.5 ftE' = 2.08 106 psi

Power Law rheology: K' = 0.022 lbf/(ft2 sec0.63) and n' = 0.63

Leakoff coefficient (w.r.t. perm zone) CL,p = 0.003 ft/min1/2

Spurt loss is negligible

Blender can do max 12 ppga

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Proppant mass for (two wings), lbm 100,000Sp grav of proppant material (water=1) 2.65Porosity of proppant pack 0.35Proppant pack permeability, md 60,000Formation permeability, md 0.5Permeable (leakoff, net) thickness, ft 45Well Radius, ft 0.328Well drainage radius, ft 3000Pre-treatment skin factor 0Fracture height, ft 67.5Plane strain modulus, E’ , psi 2.08×106

Slurry injection rate (2 wings, liq+prop), bpm 30Rheology, K' (lbf/ft2)×sn' 0.0220Rheology, n' 0.63Leakoff coefficient in perm layer, ft/min0.50.003Spurt loss coefficient, Sp, gal/ft2 0

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Ex_2 Proppant placement efficiency is 66.7%

The fracture height is 1.5 times the pay layer thickness,

therefore approximately 66,700 lbm proppant will be

placed into the pay (2 wings).

The mass of proppant in one wing will be 50,000 lbm

from which 33,300 lbm will be in the pay layer.

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Ex_2 Modified Target

Proppant mass placed (2 wing), lb 100,000Proppant in pay, (2 wing) lb 66,700Proppant number, Np 0.117Dimensionless PI, JDact 0.48 Dimensionless fracture cond, CfD 1.6 Half length, xf, ft 718 Propped width, wp, inch 0.115Post treatment pseudo skin factor, sf -6.3Folds of increase of PI 4.0

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Ex_2 Input in Consistent Units (SI)

63.0'n

Pa 10436.1 psi1008.2' 106 E

m 72.13ft 45 ph

m 57.20ft 5.67 fh 6667.0pr

m 219ft 718 fx

/sm 03975.0bpm l

/sm .002649790bpm 15 3

3

iq

0.540.5

0.5

0.5, m/s 1018.1ft/min l

m/s .03934950

min

ft 003.0

pLC

kg 012,15lbm 33,333M pay1w,

kg 22,680 lbm ,00005M1w

0.63sPa 053.1' K

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Ex_2 Modified (Apparent) Leakoff Coefficient is 2/3-rd of CL,p

The fracture height is 1.5 times the pay layer

The apparent leakoff coefficient will be only

CL = 0.667 CLp = 0.787×10-4 m/s0.5

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1 Calculate the wellbore width at the end of pumping from the

PKN (Power Law version)

2 Convert max wellbore width into average width

22

11

22

122

2222

1

0, '

14.2198.315.9

n

fn

fn

inn

n

n

n

nw E

xhqK

n

n=w

0,628.0 we ww

Ex_2 Pumping time, slurry volume (1 wing)

in. 0.252 m 0064.0 =we

in. 0.402 m 0102.00, =ww

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Ex_2 Pumping time, slurry volume (cont’d)

0)w(t)C1.5 2(txh

qeL

ff

i

The positive root of the quadratic equation is x = 43.4 s0.5 therefore the injection time is te = 43.42 s

= 31.4 min.

4 Once the injection time is known, calculate the injected slurry volume (1 wing)

gallon 810,19ft 6492,m 0.57tqV 33eii

tx

3 Assume a = 1. 5 and solve the mat balance for inj time,

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Ex_2 Efficiency

3m 8.28 efffe whxV

% 5.38385.0 i

fee V

V

Volume of 1 wing at end of pumping:

5 Fluid efficiency:

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Ex_2 Proppant concentration at end of pumping

This concentration is mass proppant per volume of slurry. We want this to be the proppant concentration everywhere in the fracture at the end of pumping. This should be the proppant concentration in the last injected slurry stage.

In terms of added proppant to clean liquid this is 1133 kg added to 1 m3 clean liquid, 70.8 lbm added to 1 ft3 clean fluid that is 9.3 ppga (lbm proppant added to 1 gallon clean fluid)

3m

33fe

1we ft

lb49

m

kg887

m 28.8

kg 22,680

V

Mc

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Ex_2 Proppant schedule

445.0385.01

385.01

1

1

e

e

33 m 8.82m 0.75445.0 ipad VV min 0.14min 5.31445.0 epad tt

445.0

3 0.145.31

0.14min

m

kg788

t

tt

ttcc

pade

pade

This is kg proppant in 1 m3 of slurry

propp

added cc

c

1

Convert it “propp-added-to-clean”

Nolte exponent

Pad

Proppconcentration

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Ex_2 Stages at end of pumping (after PWC)

1 lb/galconcentrated

to 9 lb/gal

9lb/gal

3 to 9 lb/gal

ProppantSettling

6 to 9 lb/gal 2 to9 lb/gal

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tmin

Liq_rate (2w)bpm

Cum_liqgal

Proppppga

Cum Propplbm

xfft

waveinch

0.00 30.00 0 0.00 0 0.0 0.000

14.16 30.00 17836 0.00 0 434.9 0.21614.94 28.06 18763 1.53 1,416 450.1 0.21915.73 27.15 19660 2.33 3,501 465.0 0.22116.51 26.50 20535 2.92 6,057 479.6 0.22317.30 25.98 21393 3.42 8,994 493.9 0.22518.09 25.53 22236 3.87 12,260 507.9 0.22718.87 25.13 23066 4.28 15,816 521.7 0.22919.66 24.77 23884 4.67 19,637 535.3 0.23120.45 24.44 24692 5.03 23,700 548.7 0.23221.23 24.13 25489 5.38 27,990 561.8 0.23422.02 23.84 26276 5.72 32,491 574.8 0.23622.81 23.56 27054 6.04 37,193 587.5 0.23723.59 23.30 27824 6.36 42,085 600.1 0.23924.38 23.05 28585 6.66 47,158 612.6 0.24025.17 22.82 29339 6.96 52,405 624.8 0.24225.95 22.59 30085 7.26 57,818 636.9 0.24326.74 22.37 30824 7.54 63,392 648.9 0.24527.52 22.16 31556 7.83 69,121 660.7 0.24628.31 21.95 32281 8.11 74,999 672.4 0.24729.10 21.75 33000 8.38 81,023 683.9 0.24929.88 21.56 33712 8.66 87,188 695.3 0.25030.67 21.37 34418 8.93 93,490 706.6 0.25131.46 21.19 35118 9.19 99,925 717.8 0.252

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Ex_2 Proppant Roadmap

0

5

10

15

20

25

30

35

0 10 20 30 40

Pumping time, min

Liqu

id in

ject

ion

rate

, bpm

0

1

2

3

4

5

6

7

8

9

10

ca, l

bm p

rop

adde

d to

gallo

n liq

uid

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Stage design (Injected fluid and proppant amount and rate, for two wings)

Stage Start

min

End

min

StageAddedProppantConcentrppga

StageSlurryVolume

gallon

StageProppantMass

lbm

CumLiq

gallon

CumPropp

lbm

Pad 0 21.9 0 0

1 1

2 2

3 3

4 5

5 7

6 9 150,000

Stages

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Design Outcome

Constraints allow optimum placement of the given amount of proppant

Some improvement is necessary Consider higher quality proppant

Better fluid loss control

Better rheology

Larger allowable proppant concentration

Optimum placement is not possible with traditional method: consider tip screenout design

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Additional Concerns During Design

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Screenout in the near-wellbore region:

Proppant cannot enter to the main body of

the fracture (oftentimes in Austin chalk)

Screenout at tip: Length control

Two concepts:

Enough width for a single proppant

Enough width for the actual number of proppant

grains

Tip Screenout vs. Near-well Screenout

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Width to accept proppant

At the end of pad stage the created width

has to be at least 2-3 times the proppant

diameter

At the end of pumping the proppant

reaches only that part which has a width at

least 2-3 times the proppant diameter

Propped length less than hydraulic length

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Width ratio criterion

Considering material coordinate,

Accounting for fluid loss

Calculate ratio of (Dry width) to (Dynamic

width)

Criterion: cannot exceed critical value

(about 0.5)

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Net Pressure Prediction (PKN)

Net pressure is proportional to width

Width from width equation (PKN)

Convert it to pn

Basic uses:

Feedback to height containment

Hydraulic horsepower calculation

0,2

'w

fn w

h

Ep

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Hydraulic Horsepower

Energy: (Power) (Time)

Power = (Pumping Pressure) (Injection rate)

(Pumping Pressure) =

Minimum Stress + Net Pressure + Friction Losses -

Hydrostatic Pressure

Friction Losses : in tubulars, through perforations

and possibly in near wellbore tortuous flow path

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On-site Tuning of Design During Job Execution

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Main Tasks During Execution

Zonal Isolation, Cement Integrity Perforation strategy Pumping through tubing, casing, both Safety considerations: wellhead, casing, tubing Formation breakdown and Step rate test Calibration test (Minifrac) Pad and Proppant schedule tuning Pumping Monitoring: Tip screenout - near-well/well screenout Flush Forced closure Cleanup

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Perforation and Execution Strategy

For thin layer: Perforate the whole interval

For thick or multilayer formationDanger: non uniform coverage

Solution: Ball sealers, Limited entry or Staged

Limited entryFew perforations in small groups

High perforation friction loss

Uniform coverage

Staged (from bottom to top)

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Design Tuning Steps

Step Rate test

Minifrac (Datafrac, Calibration Test)

Run design with obtained min (if needed)

and leakoff coefficient

Adjust pad

Adjust proppant schedule

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Introducing…

HF2DPKNHF2DPKN

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Input Parameters

Proppant mass for (two wings), lbm

This is the single most important decision variable of the design procedure

Sp gravity of proppant material (from 2.6 to 3.5)

Porosity of proppant pack (e.g. 0.35)

Proppant pack permeability, md

One of the most important design parameters. Retained permeability including fluid residue and closure stress effects, might be reduced by a factor as large as 10 in case of non-Darcy flow in the frac Realistic proppant pack permeability would be in the range from 10,000 to 100,000 md for in-situ flow conditions. Values provided by manufacturers such, as 500,000 md for a “high strength” proppant should be considered with caution.

Max prop diameter, Dpmax, inch

From mesh size, for 20/40 mesh sand it is 0.035 in.

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Input Parameters cont'd Formation permeability, md Permeable (leakoff) thickness, ft Wellbore Radius, ft Well drainage radius, ft

Needed for optimum design. (Do not underestimate the importance of this parameter!)

Pre-treatment skin factor Can be set zero, it does not influence the design. It affects only the

"folds of increase" in productivity, because it is used as basis.

Fracture height, ft Usually greater than the permeable height. One of the most critical

design parameters. Might come from lithology information, or can be adjusted iteratively related to the frac length.

Plane strain modulus, E' (psi) Hard rock: about 106 psi, soft rock 105 psi or less.

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Input Parameters cont'd

Slurry injection rate (two wings, liq+ prop), bpm

Rheology, K' (lbf - secn'/ft2)

Rheology, n'

Leakoff coefficient in permeable layer, ft/min0.5

The leakoff coefficient outside the permeable layer is considered zero. If the frac height to permeable layer ratio is high, the apparent leakoff coefficient calculated from this input will be much lower than the input for this parameter. If the leakoff is significant outside the net pay, you may want to adjust this parameter when you adjust fracture height.

Spurt loss coefficient, Sp, gal/ft2

The spurt loss in the permeable layer. Outside the permeable layer the spurt loss is considered zero. See the remark above.

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Input Parameters, cont'd

Max possible added proppant concentration, lbm/gallon fluid (ppga) The most important equipment constraint. Some current

mixers can provide more than 15 lbm/gal neat fluid. Often it is not necessary to go up to the maximum technically possible concentration.

Multiply optimum length by factor This design parameter can be used for sub-optimal design.

Play!

Multiply pad by factor Play (if necessary)!

(More input for TSO, Cont Damage Mech, etc.)

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Summary

Keep in mind the goals

Allocate resources according to significance

Realize need for compromise:

Limited data

Limited understanding of physics

Sensitivity to the uncertainty in data

Find the optimum complexity of model

Do sensitivity analysis

Make decisions top - down

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Computer Exercise 2-1: Medium perm design example

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Computer Exercise 2-2: Tight gas design example

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Computer Exercise 2-3: High perm Frac&pack example