tfs2
TRANSCRIPT
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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