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• Introduction and the need for unconv entional resources • Ne Need ed for numerical modelling of un conventional reservoirs • Various aspects of unc onventional reservoir modelling – – – – –
Natural fracture modelling Gas adsorption in shale Gas diffusion Hydraulic fracture modelling Micro-sesimic data • Plan anar ar fr frac acttur ures es • Compl Complex ex fracture fractures s and and Stimul Stimulated ated Reser Reservoir voir Volume olumes s – Non-Darcy flow of gas
• IMEX or GEM? • CM CMOS OST T based parameterization parameterization and w ork flow
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• Shale gas gas and oil o il • Tight gas and and oil oi l • Na Natu tural ral gas g as from fr om co coal al (NGC/C (NGC/CBM/CS BM/CSG G etc.) • Ga Gas s hydrates hy drates or Me Methane thane hydrates hydr ates
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• In the the past, past, techn technical ical challe challenges nges and cost issues around producing unconventional gas deterred resource exploration and development. • However However,, as conve convention ntional al gas gas resour resources ces are becoming depleted and the need for energy has increased, the necessity for developing alternate resources has become important. i mportant. • Although Although prod productio uction n of uncon unconventi ventional onal gas in Canada is very recent, it is anticipated that by 2025, unconventionall gas will account for about 80 per unconventiona cent of new drilling and 50 per cent of total gas production.
• Our known known conve conventi ntiona onall sources sources of natur natural al gas in in North North America are declining rapidly. rapidly. • Acc Accordi ording ng to the the Nation National al Energy Energy Board Board (NEB), (NEB), gas gas production in Canada peaked at 17.5 bcf/d in 2001, and has been decreasing since then. • New gas gas finds finds are neede needed d every year year simpl simply y to offse offsett a 6.5% natural decline rate in production from existing wells. • With demand for natural gas expected expected to remain remain strong for the foreseeable future, most, if not all of the available new supply sources will be required to meet consumer demand in North America. • Ind Indust ustry ry and gover governme nment nt see Uncon Unconven ventio tional nal gas as as having an important role in reducing the gap between future demand and declining conventional production.
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Conventional natural gas supply decline that must be found from new sources such as tight and shale gas
Source: NEB website
Source: NEB 2011
Tcf/y
History
40
Bcf/d
Projections
2012
100 90
35
80 70
30
60
25
50
Shale gas
20
40 30
15 10 5
20
Tight gas
Non-associated onshore
10
Non-associatedoffshore
0 1990
Associated with oil Coalbed methane
1995
2000
2005
2010
2015
2020
2025
2030
Alaska
2035
0
2040
Source: EIA, Annual Energy Outlook 2014 Early Release
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31/08/2015
Light oil production decline that must be found from new sources such as tight oil, shale oil and liquid rich unconventional gas
Source: NEB website
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U.S. shale & tight oil production (mmbpd)
U.S. dry shale gas production (bcfd) 2.8
35
Eagle Ford(TX) Bakken (MT& ND)
2.4
Restof US Marcellus (PAand WV)
30
Granite Wash (OK& TX)
2.0
Haynesville (LAand TX)
25
Bonespring (TX Permian)
Eagle Ford(TX)
Wolfcamp(TX Permian) Spraberry(TX Permian)
1.6
Niobrara-Codell (CO)
1.2
Woodford (OK) Monterey(CA)
Bakken(ND) Fayetteville (AR) Barnett (TX)
0.8
Austin Chalk (LA & TX)
Antrim (MI, IN, and OH)
0.4
15 10 5
0.0 2000 2002 2004 2006 2008 2010 2012
20
Woodford (OK)
0 2000 2002 2004 2006 2008 2010 2012
Source: EIAbased on DrillingInfo and LCI Energy Insight
• • • • • • • • • • • • • • • • • • • • • • • • • • • • •
Antrim (Michigan) Bakken (Montana, N. Dakota, Saskatchewan, Manitoba) Baxter (Colorado, Wyoming) Barnett (Texas) Bend (Texas) Cane Creek (Utah) Caney (Okla homa) Chattanooga (Alabama, Arkansas, Kentucky, Tennessee) Chimney Rock (Colorado, Utah) Cleveland (east Kentucky) Clinton (east Kentucky) Cody (Montana) Colorado (central Alberta, Saskatchewan) Conasauga(Alabama) Duvernay (west central Alberta) Eagleford(Texas) Ells worth (Michigan) Excello (Oklahoma) Exshaw (Alberta, northeast British Columbia) Fayetteville (Arkansas) Fernie (west central Alberta, northeast British Columbia) Floyd/Neal (Alabama, Mississippi) Frederick Brook (Nova Scotia) Gammon (Montana) Gordondale (northeast British Columbia) Gothic (Colorado, Utah) Green River (Colorado, Utah) Haynesville/Bossier (Louisiana, east Texas) Horn River (northeast British Columbia)
Horton Bluff (Nova Scotia) Hovenweep (Colorado, Utah) Huron (east Kentucky, Ohio, Virginia, West Virginia) Klua/Evie (northeast British Columbia) Lewis (Colorado, New Mexico) Mancos (New Mexico, Utah) Manning Canyon (central Utah) Marcellus (New York, Pennsylvania, West Virginia) McClure (California) Monterey (California) Montney-Doig (Alberta, northeast British Columbia) Moorefield (Arkansas) Mowry (Wyoming) Muskwa (northeast British Columbia) New Albany (Illinois, Indiana) Niobrara (Colorado) Nordegg/Gordondale(Alberta, northeast British Columbia) Ohio (east Kentucky, Ohio, West V irginia) Pearsall (Texas) Percha (west Texas) Pierre (Colorado) Poker Chip (west central Alberta, northeast British Columbia) Queenston (New York) Rhinestreet (Appalachian Basin) Second White Specks (southern Alberta) Sunbury (Appalachian Basin) Utica (New York, Quebec) Wilrich/Buckinghorse/ Garbutt/Moosebar (Alberta, British Columbia) Woodford (Oklahoma, Texas)
Red – CDN Common, Black – other CDN, Blue - USA
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Source: EIA website
• Barnett Shale – 6000+ wells – MANY have marginal economics
• Horn River Basin – 1 million acres • Montney Shale – 17 million acres – Estimated 10,000 wells to be drilled in this play – EnCana est. 60 TCF on it’s lands
• “ Haynesville Shale Primed t o Become World's Largest Gas Field by 2020” – Largest well 28.4 mmcf/d
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• Strict cost control is an overriding concern in most operations, yet there are tangible economic benefits for operators who make the effort to model reservoir performance before they drill. - i.e. Spend a ½ day in the Library rather than waste $1mm • Need to fully understand the underlying physics that govern the methane release and flow in the shale. • Determine optimal well spacing and optimal frac size & spacing. • Are vertical or horizontal wells the economically optimal solution? Jenkins & Boyer, JPT, Feb 2008 • Size fracs to avoid breakthrough to water. • Crucial to identify the reservoir parameters that will have the most impact on project economics. (sensitivity analysis)
12 pumping units 66 – 400bbl tanks = 1.1mm gal PER STAGE!
$$$$$$$$$$$$$$$$$$$
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400 ft gap
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$250k per frac stage, 6 to 20 stages per well $1.5MM to $5MM per well What would you pay to get it right? 0.8bcf * $4.10/mcf * 1,000,000 = $3.3MM lost 0.8 Bcf SPE 119899 : 69% of 389 wells completed in the Barnett study have less than a 10% internal rate of return !
SPE 102103
Advanced Processes & Thermal Simulator Compositional & Unconventional Reservoir Simulator Three-Phase, Black-Oil Reservoir Simulator Sensitivity Analysis, History Matching, Optimization & Uncertainty Analysis Tool Integrated Production & Reservoir Simulation Intelligent Segmented Wells Phase Behaviour and Fluid Property Application Pre-Processing: Simulation Model Building Application Post-Processing: Visualization &Analysis Application
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Reservoir Descri ption • Matrix – intrinsic porosity & absolute permeability • Natural Fractures – dual permeability representation with effective fracture porosity & effective fracture permeability • Propped Fractures – explicitly modelled as part of matrix • Pore Volume Compaction/Dilation – via constant compressibility and/or compaction/dilation tables • Momentum Transfer – Darcy and Non-Darcy (Turbulent) Flow, the latter in the propped fractures
PVT • Black Oil (IMEX) – for black oil and dry gas • EoS – for wet gas, gas condensates (lean and rich) and volatile oil
Adsorbed components • Gas phase only – for mostly methane tight/shale gas • Multi-component – for multi-component gases (w/impurities) & liquids
Diffusion • Multi-component gas • Miscible Gas Injection EOR
Rock Physics • Tight rock Rel Perm & Cap Press in matrix • Straight Line Rel Perm & no Cap Press for propped & natural fractures
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Simulation Model Griddi ng • Logarithmically-Spaced, Locally-Refined, Dual Permeability (LS-LR-DK or Tartan) Grids surrounding the propped fractures ‒
‒
For modelling transient multiphase fluid flow (and heat, if desired) from matrix to natural fractures & from matrix to propped fractures For modelling non-Darcy flow inside the propped fractures
Simulation Model Initialization • Initializing the propped & natural fracture network with water ‒
For modelling flowback of injected fracture fluid
Why? • Shale acts as both sourc e / reservoir rock. • Therefore, Gas in shales is found in two forms: Free Gas - Gas stored in matrix pore volume
•
Adsorbed Gas - Gas is attached or ADSORBED onto solid organic material in the shale
Let’s look at Shale gas modell ing only. The concepts learned can be applied to any unconventional resource modelling
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Natural Gas stored in organic rich rocks:
Shale Shaly Siltstone Shaly Sandstone
• Generally Naturally Fractured
Low permeability fractures
• Matrix extremely l ow permeability
Range from micro to nanodarcies
• Pore Diameters are extremely s mall
Range from micro to nanometres
Conventional Gas
Shale Gas
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• Horizontal wells: To maximize contact area • Multi-stage fracturin g: 10-30 fractures per well
Source: thebreakthrough.org
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Hydraulic Fracture Treatments Pumping Phase
N
Hydraulic fracture resumes in S Hmax direction at natural fracture tip
Reactivation of natural fractures
Trace of part of horizontal wellbore with perforation
J.F. Gale, UT, 2008 ~ 500 ft
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Standard dual-porosity model
MINC model
Dual-permeability model
Subdomain partitioning
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• Shale has both Darcy flow and diffusion in matrix as opposed to just diffusion in coal • Simulator must handle both Darcy flow and multi-component diffusion in the matrix block. Storage: Adsorbed and free gas in matrix.
Gas Flows into the F racture b y: 1). Darcy Flow: Owing to pressure gradient and small permeability of m atrix. 2). Instantaneous desorption from internal surfaces of matrix- followed by darcy flow.
Shale Gas Reservoir
Gas flow through the Shale Matrix by: • Darcy flow • Diffusion Gas Flow in Fractures: • Darcy flow • Non-Darcy flow Incorporate 3 flow regimes
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• Free gas • Solution gas (in (in case of shale oil reservoirs) • Ad Adso sorb rbed ed gas • Si Simi mila larr to CB CBM M res reserv ervoi oirs rs
GIP GI P = Free gas + Solution Solut ion gas + Adsorbed Adso rbed gas g as Typically > 95% for CBM reservoirs ~ 20 – 70% for Shale Shale gas reservoirs reservoirs
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• Ads or pt io n of gas in cr eases no n-l in earl y w it h pres p res su re an d i s reversible reve rsible by decrea decreasing sing the pressure •
Represente Re presented d by Langmuir adsorption isoth erm using two pr operties: – Langmuir volume (VL) – Langmuir pressure (PL)
• At kn ow n reser r eser vo voir ir T and P, an i so th erm can be u sed to est im ate t he max. amount of gas adsorbed in shale & the pressure at which desorption will start Typical Shale Adsorption Curve 700
) n o t 600 / 3 t f ( 500 n o i t 400 p r o s 300 d A s 200 a G
100 0 0
1 00 0
2 00 0
30 00
40 00
Pressure (psi)
1,000
Considering Adsorbed Gas
20%
800
) y a d / f c M ( C S e t a R s a G
1,500,000
) f c M (
Not Considering Adsorbed Gas 600
C
1,000,000 S
s a G e v i t a l u m u C
400
500,000 200
0 0
2,000
4,000
6,000
8,000
0 10,000
Time (day)
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6,000,000
5,000,000
4,000,000 ) f c M ( C S s a G3,000,000 e v i t a l u m u C2,000,000
New Albany Shale Barnet Shale 1 Barnet Shale 2 Client "X' shale data
1,000,000
0 0
2,000
4,000
6,000
8,000
10,000
Time (day)
BUT THIS REQUIRES REQUIRES DRAWDOWN DRAWDOWN !!! !! !
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Single component adsorp tion: – Requires Langmuir Volume, VL (i.e. Max. adsorbed gas) – Langmuir Pressure, PL (represents the pressure at which gas storage capacity equals one half of the maximum storage capacity (VL ).
i
V P L P L P
Where, ωi = Gas content – Volume of adsorbed gas per unit mass of rock (IMEX) – Moles of adsorbed gas per unit mass of rock (GEM)
•
IMEX
ADGCSTV- inverse-pressure parameter for the Langmuir isotherm (1/PL) –
•
•
•
1/kPa or 1/psi
ADGMAXV- Specifies the maximum volume of adsorbed gas per unit mass of rock (VL)
GEM
ADGCSTV (IMEX); ADGCSTC (GEM) – inverse-pressure parameter for the Langmuir isotherm (1/PL) – 1/kPa or 1/psi
•
ADGMAXC- Specifies the maximum moles of adsorbed component per unit mass of rock (VL)
–
sm3 gas/kg of rock or sft3 of gas / lb of rock
– gmole of component/kg of rock or gmole of component/lb of rock
–
(Watch out for the right unit !!!!)
– (Watch out for the right unit !!!!)
ROCKDEN : Coal Density (Actual Rock Density without pore) –
kg/m3 or lb/ft3
•
ROCKDEN : Coal Density (Actual Rock Density without pore) – kg/m3 or lb/ft3
•
These keywords must be in the ROCK-FLUID section of the dataset.
•
Typically only one component (Methane) for shale gas simulations in GEM
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Multi-component adsorption model: – Extended Langmuir model
i
i , max
( y ig p / p Li ) 1
( y jg p / p Lj ) j
Where, yig = mole fraction of adsorbed component in the gas phase.
– Based on Langmuir isotherm for single components – Provides a multi-component extension
E.g. **$ Property: Maximal Adsorbed Mass(CH4) (gmole/kg) Max: 0 Min: 0 ADGMAXC 'CH4' FRACTURE CON 0 **$ Property: Maximal Adsorbed Mass(CO2) (gmole/kg) Max: 0 Min: 0 ADGMAXC 'CO2' FRACTURE CON 0 **$ Property: Maximal Adsorbed Mass(CH4) (gmole/kg) Max: 0.734287 Min: 0 ADGMAXC 'CH4' MATRIX CON 0.734287
Langmuir Isotherm keywords: • Fracture adsorbed mass always 0 • Matrix values for adsorb ed mass, Langmuir constant, and rock density • Different values for different components • Keywords can be constants or arrays for the grid
**$ Property: Maximal Adsorbed Mass(CO2) (gmole/kg) Max: 1.04824 Min: 0 ADGMAXC 'CO2' MATRIX CON 1.04824 **$ Property: Langmuir Adsorption Constant(CH4) (1/kPa) Max: 0.000303306 Min: 0.000303306 ADGCSTC 'CH4' MATRIX CON 0.000303306 **$ Property: Langmuir Adsorption Constant(CH4) (1/kPa) Max: 0 Min: 0 ADGCSTC 'CH4' FRACTURE CON 0 **$ Property: Langmuir Adsorption Constant(CO2) (1/kPa) Max: 0.000809717 Min: 0.000809717 ADGCSTC 'CO2' MATRIX CON 0.000809717 **$ Property: Langmuir Adsorption Constant(CO2) (1/kPa) Max: 0 Min: 0 ADGCSTC 'CO2' FRACTURE CON 0 **$ Property: Rock Density (kg/m3) Max: 1327 Min: 1327 ROCKDEN MATRIX CON 1327
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• Options for other complex adsorption models – Tabular input for more complicated systems
Syntax for tabular adsorpt ion data entry ADSORBTMAX ‘component’
ϖmax
Where, ϖmax = maximum adsorption value for the component in gmole/kg( or lb) of rock.
ADSTAB ‘component name’ ** (Partial pressure of component, kpa/psia)
(adsorption of component)
ω ω ω
…
…
ω
• In case of multi-component system, this table can be extended for each component.
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Sample Conversion of Adsor bed Mas • Simulator: IMEX • Unit: SI • Lab measurement: VL = 167 SCF/ton, convert to sm3/kg
167
.
∗
∗
.
0.00521 3/
• The Langmuir volu me can be converted to mole basis using the ideal gas equation, std. temp. and press. (for GEM only) • Molar Volume= RT/P (cm3/gm ole) Where, Universal gas constant, R = 82.05 cm3.atm/gmole.K T = Temperature in K. P = pressure in atm. • ADGMAXC (gmole/k g)= V L (cm3/kg)/Molar Volume (cm3/gmo l) Lab data (VL )typically reported at STANDARD cond itio ns (e.g. SCF/ton ) • This formula can be constructed using the “ Formula” option in BUILDER.
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Sample Conversion of Adso rbed Mas • Simulator: GEM • Unit: SI • Lab measurement: VL = 167 SCF/ton , conv ert to gmo l/kg • Standard Condition s: T= 60 °F= 15.55 °C= 288.7 K P: 1 atm R: 82.05 cm3*atm/(gmol*K) Molar Volume = RT/P = 23688.29 cm 3/gmol 167
•
.
∗
∗
.
∗
.
0.22 /
Test Simulation on a 1 microdarcy shale reser voir has show n the p res su re d is tu rb an ce ar ou nd t he f rac tu re ex ten di ng as l ow as o nl y ~ 300 ft after 30 years of production.
SPE102103 Mayerhofer et al.
(similar work done by Fekete in 2007)
•
Th er e ar e t hr ee m ai n c on cl us io ns t hat c an b e t ak en f ro m t hi s : • Minimal gas desorbed from the outer region of the contacted area due to the small change in reservoir pressure. • Tight well spacing & a dense fracture network are required to reduce the reservoir pressure enough to desorb MEANINGFUL amounts of gas. • Gas will desorb from the areas exposed to the fractures due to the high drawdown created at the fracture face.
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• Avail abl e in on ly GEM • Ac ces si bl e th ro ug h Bui ld er t oo , in Com po nen ts section GEM gas diff usion k eywords: DIFFUSION tortuo (diffus(k), k = 1, 2 .. Nc Where, tortuo = Tortuosity of porous medium, dimensionless diffus = Diffusion coeff. for hydrocarbon components, be in cm2/sec ONLY
26
31/08/2015
• Can contribute to overall gas flow in case of multiple components
∗
∗ ∗ ∗ ,, ,,
15%
4.00e+6
3.00e+6
) f c M (
C S s a G e v i t 2.00e+6 a l u m u C
Diff: 0.0003 cm2/sec Diff: 0.003 cm2/sec Diff: 0.006 cm2/sec Diff: 0.03 cm2/sec
1.00e+6
0.00e+0 0
2,000
4,000 Time (day)
6,000
8,000
10,000
27
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31/08/2015
Trend visible in red stage
Possible trend visible in blue stage
In-situ stress will influence dominant hydraulic fracture orientations Shmax direction?
Possible interaction with preexisting fractures?
Williams-Stroud, Microseismic, 2008
300m x 300m grid Fracture size can be related to event moment magnitude, defined as:
450m fracture
M 0 = mSd
Where m = rigidity S = fracture area d = displacement
200m fracture
360m fracture
Estimates of size of the fracture planes and the slip patch are consistent with other published estimates (Barton and Zoback, 1994)
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• Natural fr actures and matrix flow are handled by DUALPERM model • Adsorption is handled by Langmui r is otherm • Gas-phase diffusi on is handled by specifying the tortuosity and diffusion coefficient. • Non-Darcy f low in hydraulic fractures: – At high velocities, fluid flow deviates from what would be expected with Darcy’s Law – More resistance to flow at higher velocities
• Conventional fractured reservoirs typically can be modelled using standard Dual Porosity/Permeability or MINC Models • Due to the extremely slow pressure transients in shales and other tight reservoirs, flow cannot be accurately described using these standard models • Hydraulic Fractures need to be explicitly modelled to model the flow behavior • To model the transients accurately
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• A simple estimate of the end of the transient response period is (from L. H. Reiss): ∆
∗ ∗∗∗
Where, • DIFRAC is in cm • is in fraction • is in cP • is in bar -1 • is in md
• For • • • • •
DIFRAC = 150 ft = 5% = 0.02 cP = 1e-4 1/bar = 1e-5 md
T = 500 x 45722 x 0.05 x 0.02 x 1e-4/1e-5 T = 3.3 years • (normally this is less than two minutes for a 10 md matrix)
• In the reservoir, the hydraulic fractures have width s in the magnitude of a couple millimeters with very high intri nsic permeabili ties • To model thi s, very fine griddi ng woul d be required – With more grid blocks, runtimes will become very large
• To reduce the number o f bl ocks and the runti me, the fracture can be pseudoized to a width of 2 ft – Permeability of the hydraulic fractures is replaced with an effective permeability – LS-LR-DK Method (SPE 132093) • Logarithmically Spaced, Locally Refined, Dual-Permeability
31
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Pinnacle Technologies Microseismic Fracture Map 1,200
Modeled with high density fracture network in GEM
1,000
) y a d / f c M ( C S e t a R s a G
800
600
H.F. Horizontal Well
400
Not H.F. Horizontal Well
200
0 0
2,000
4,000
6,000
8,000
Time (day)
Planar fractures in SRV
Complex fractures in SRV
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31/08/2015
Create LS-LR-DK grids aroun d fractures automatically
Single Plane Geometry
Complex Geometry
Propped Frac Properties: Half-length, Width, Perm, Spacin g, Height & Perm Gradient Stimulated Natural Frac Properties: Width, Perm
SRV Size & Shape: # MS events p er gridbl ock MS Moment Magnitude MS Conf idenc e Value ?
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Qoriginal=Qnew Kf wf hf /μ*(dP/dx)=Keff weff hf /μ*(dP/dx) Kf wf =Keff weff Keff =Kf wf /weff
• To correctly capture the transient effects around the hydraulic fractures, fine gridding of the matrix is required • Local Refinement is used around the fractures to have more accuracy where it is needed • Evenly spaced gridding has too much accuracy far away from the fractures where it is not needed and not enough accuracy close to the fracture • Logarithmic Refinement solves this issue by having more refinement close to the fracture where it is needed and less refinement far away from the fracture
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Pressure (kPa) 2000-04-30
-100
K layer: 1
0
Scale: 1:1192 Y/X: 0.60:1 Axis Units: m
100
0
0
15,051 14,470 13,888 13,306 12,724 12,142 11,561 10,979 1 0 0
0 0 1 -
10,397 9,815 9,234 8,652
Well-1
8,070 7,488 6,907 6,325 5,743 5,161 2 0 0
0 0 2 -
4,579 3,998 3,416 2,834 2,252 1,671 1,089
-100
0
Pressure (kPa) 2000-04-30
-100
507
100
0
K layer: 1 Scale: 1:1192 Y/X: 0.60:1 Axis Units: m
100
0
0
15,051 14,470 13,888 13,306 12,724 12,142 11,561 10,979 1 0 0
0 0 1 -
10,397 9,815 9,234 8,652
Well-1
8,070 7,488 6,907 6,325 5,743 5,161 2 0 0
0 0 2 -
4,579 3,998 3,416 2,834 2,252 1,671 1,089
-100
0
100
507
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Pressure (kPa) 2000-04-30
-100
K layer: 1
0
Scale: 1:1192 Y/X: 0.60:1 Axis Units: m
100
0
0
15,051 14,470 13,888 13,306 12,724 12,142 11,561 10,979 1 0 0
0 0 1 -
10,397 9,815 9,234 8,652
Well-1
8,070 7,488 6,907 6,325 5,743 5,161 2 0 0
0 0 2 -
4,579 3,998 3,416 2,834 2,252 1,671 1,089
-100
0
507
100
Pressure Profile Around Fracture 15,000
Too much Refinement Far From Fracture
10,000
) a P k ( e r u s s e r P
5,000
Not Enough Resolution Close to Fracture 0 1,922
1,942
1,962
1,982
2,002
2,022
2,042
Distance (m) Fine Scale Gridding Even Gridding
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Pressure Profile Around Fracture 15,000
Lower Resolution Far from Fracture
10,000
) a P k ( e r u s s e r P
5,000
High Accuracy Close to Fracture 0 1,922
1,942
1,962
1,982
2,002
2,022
2,042
Distance (m) Fine Scale Gridding Logarithmic Gridding
Cumulative Gas Production 4.00e+6
3.00e+6 ) 3 m ( C S s a 2.00e+6 G e v i t a l u m u C
1.00e+6
0.00e+0 2000-1- 1
2000- 1- 21
2000- 2- 10
2000- 3- 1
2000- 3- 21
2000- 4- 10
2000-4
Time (Date) No Refinement (90 m Gridding) Even Gridding Logarthimic Spacing Fine Gridding
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• Reference Models created with explicitly modelled fractures using their true width (both hydr aulic and natural fr actures) to valid ate LS-LR-DK method • 5-14 Million Grid Cell Model • Models require several hours to run • Not practical for normal simulation work
• LS-LR-DK model with 9x9 refinement around hydraulic fractures
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• Grid with 9x9 refinement around hyd raulic fractures compared against reference model – Less than 3 minute runtime – Results very close to reference solution
39
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• In the past we have normally used factor correlations from Geertsma or Fredrick and Graves • These correlations do not directly apply to propped fractures • Newer Correlations have been proposed for fractures which are not explicitly a strong function of saturation • These correlations have the form shown below and are far easier for the simulator to work with – The simulators can use these correlations simply by setting N2p = 0
p
p
K K
N1 p
rp
• The correlation for b developed by Cooke, C.E. “Conductivity of Fracture Proppants in Multiple Layers” J.Pet.Tech, (Sept 1973) pp1101-1107 is relevant for fractured systems and is presented below (bfrac in 1/ft, Kf in mD). Perms varied from 5,000 – 30,000 md Proppant Sand Mesh Size
(p)
N1(p)
8-12 (highest Perm)
538.108E9
1.24
10-20
850.525E9
1.34
20-40
3411.752E9
1.54
40-60 (lowest Perm)
2143.503E9
1.60
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• Cooke’s correlation predicts very large non-Darcy effects in shales as it is based on more heterogeneous crushed sand (higher turbulence due to packing of d ifferent sized sand) • A new er correl ation by Evans an d Civan (1994) DOE/BC/14659-7 was proposed: – Evans and Civan collected a total of 183 data points in this work. – In addition to the data discussed in their paper they also employed data from Geertsma in consolidated media, and – from Evans & Evans and Whitney for the effects of immobile liquid saturation
• The regression line thro ugh all the data is shown next • with correlation co efficient R = 0.974. Since thi s co rrelation is obtained from a large variety of porou s media under different condit ions, it is expected to p rovide a reasonable estimation
p
1.485 E 9 K
1.021
We assume in the fracture porosity = 1.0
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• For a 5,000 md shale gas fracture (5 md-ft cond uctiv ity and 0.001 ft fracture width) – Evans and Civan’s values are anywhere from 10 to 60 times smaller than Cooke’s, depending on proppant sand mesh size – Only when Kf approached 300,000 md do the models produce similar results (for the largest sand mesh size)
• Ideally you shou ld be able to produc e Beta factors fr om a lab experiment, but this may not be practically possible • Evans and Civan correlation r ecommended for Hydraulic Fracture modelling: –
αp:
1.485e9
– N1p: 1.021 – N2p: 0
• Resistance to Flow i s related to velocity – Deviation from Darcy’s Law only occurs at high velocities – Resistance Factor=1/(1+Fo)
• Since a larger width i s used for the hydr aulic fractu res, the velocity calcul ated will be lower – Therefore non-Darcy flow will be calculated incorrectly if no corrections are made – Forchheimer Equation Beta Correction: NDARCYCOR
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• With correction factor added (NDARCYCOR), models match the reference solution very well
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• Microseismic (MS) data acquired by some operators to monitor (even control) the treatment* can be used as a first order estimate of the extent of the unpropped SRV during pumping & the geometry of its fractures • MS data is easily incorporated into BUILDER’s model creation workflow using it’s MS Import Wizard
* Reference: George King’s SPE course
• MS data can be incor por ated into th e fracture or SRV creation process. • Estimate height and half-length of fracture • Estimate total stimulated reservoir volume (SRV) of a complex fracture network
• Does grid already exist? – If a grid exists, this can be imported – Otherwise, a simple grid can created based on MS data
•
Micros eismic Data Manager – Imports and export of Microseismic Data • XML format, CMG format, text, excel – Wizard guides users through the process – Can import customized properties such as moment, confidence etc.
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Add SRV st ages or pl anar st ages bas ed o n MS d ata
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Physics
IMEX
GEM
PVT
BO, VO, GC, WG, DG
EOS
Ads orb ed Comp onen ts
Gas Phase
Mult i-Com p
Molecular Diffusion w/ Dispersion
-
Multi-Comp/OWG Phases
Natural Fracs (NF)
Dual Perm
Dual Perm
Propped Fracs (PF)
LS-LR in Matrix (MT)
LS-LR in Matrix (MT)
Non-Darcy (turbulent) Flow
MT, NF & PF
MT, NF & PF
Non-Darcy (slip) Flow
-
MT
Krel & Pc
MT, NF, PF & time
MT, NF, PF & time
Pr es s-dependent Com pac tion
MT, NF, PF & t im e
MT, NF, PF & t im e
Stress-dependent Compaction
-
Geomechanics-based
Chemical Reactions
-
Ion Exchange & Geochemistry
Primary Production
Primary Production & EOR
‘Easy’ fluids: DG, BO
‘Complex’ fluids: GC, VO
• Matrix – Shale rock, not including fractures • Natural fracture - Fractures in the reservoir that have not been affected by the hydraulic fracture stimulation • Hydraulic Fracture - Stimulated fractures with high conductivity that have been created during the hydraulic fracture stimulation. (Sometimes referred to as the primary fracture) • Secondary Fracture (optional) – region of enhanced natural fractures in the SRV. – Conductivity usually somewhere in between the natural fractures and the hydraulic fractures
Simulator classification: MATRIX – Matrix continua – Contains Matrix and Hydraulic Fracture
FRACTURE – Fracture continua – Contains Natural Fracture and Secondary Fracture
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• Builder interface updated for use with new fracture keywords system Old Interface New Interface
• Select between ‘Planar Fracture Stage’ and ‘Complex Fracture Stage’ • Images and descriptions added to avoid confusion
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• Select Template to use or create a new one • Set spacing or location of fractures
• Typically many fractures have the same settings applied to them • Now users can create one template and apply it to multiple fracture stages or wells
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•
Templates on individual fractures can be modified
•
Property values can be overridden on an individual fracture basis
• Set different rel-perm curves for matrix and fracture (natural and hydraulic fractures) : RTYPE – Set up different rel-perm curves in the rock fluid section: One for matrix (1), one for natural fractures (2) and one for hydraulic fractures (3) – Assign values to different areas using formulas • X0=Forchheimer Equation Beta Correction • Rel Perm Set Num = if ( X0 > 0 ) then ( 3 ) else ( 1 ) • Rel Perm Set Num – Fracture = 2
• Set pressure dependent permeability curves for different regions : CTYPE – Same formula as above can be used
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• Ad ju st water s atu rat io ns in hydr aul ic fr act ur es t o ac coun t for water injected dur ing stimu lation • Fracture conduct ivity may vary vertically. – Proppant might settle in the lower portion of the fracture – Fracture conductivity may increase from top to bottom
• Natural fracture cond uctiv ity mig ht be greater near stimulated region Max. value stim. region
near
Property Sw or NF conductivity
Linear gradation towards fracture tip
Constant matrix value
Distance from well
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• CMOST can perform a variety of tasks • We will focus on t he application of CMOST with shale gas – Specifically with History Matching
• A ful l CMOST Course is available if you are interested
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CMOST is CMG software that works in conjunction with CMG reservoir simulators to perform the following tasks: Sensitivity Analysis • Better understanding of a simulation model • Identify important parameters
History Matching • Calibrate simulation model with field data • Obtain multiple history-matched models
Optimization • Improve NPV, Recovery, … • Reduce cost
Uncertainty Analysis • Quantify uncertainty • Understand and reduce risk 119
Parameters x 1, x 2, …, x n
Simulation Model y 1=f 1( x 1, x 2, …, x n) y 2 =f 1( x 1, x 2, …, x n) … y m=f 1( x 1, x 2, …, x n)
Objective Function s y 1, y 2, …, y n
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Experimental Design & Optimization Al gori thms
Select combination of parameter values
Substitute parameter values into simulation dataset
Anal yze r esu lt s
Objective Functions & Proxy Analysis
Parameterization
Run simulation 121
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Define what data to be extracted from simulation (Plots and Formulas) Define how the simulation model is parameterized (Inputs) Define objective functions to be calculated (Outputs)
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•
Parameters are variables in t he simul ation model that will be adjust ed when creating new datasets - E.g. Porosity, permeability, etc.
•
To determine the loc ation in the dataset to substi tute values, a master dataset must be created (.cmm)
• A master dataset is al most id entical to a norm al simulation dataset except CMOST keywor ds have been added to identi fy where a parameter shoul d be added - Acts as a template for creating new datasets
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• A master dataset can be created in mul ti pl e ways: • CMOST Editor • Builder • Text editor (Notepad, Textpad, etc.)
Original Dataset: POR CON 0.20 Master Dataset: POR CON this[0.20]=Porosity
Simulator Keywords
CMOST Start
No Spaces in CMOST Portion
Original (Default) Value in Dataset
Variable Name
CMOST End
Variabl e Names Case Sensi tive
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• An Objective Functi on (OF) is something (an expression or a single quantity) for which you wish to achieve some goal • Usually this goal is to achieve a minimum o r maximum value • In the case of History Matching, one usually wishes to minimize an error between field data and simulation • In the case of Optimization, one usually wishes to maximize something like NPV
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•
Basic Simulation Results • Values directly taken from simulation results with no modification • History match error • Percentage relative error • Perfect match: 0% • Net Present Value • Simplified NPV calculation • Can be used to construct user-defined objective functions which utilize simulation results discounted by time as variables
•
Characteristi c Date Times • Specific Dates • Date where maximum or minimum value is found • Date when value surpasses a specified criteria • Advanced Objective Functi ons • User defined objective function based on formula or code (jscript or python) • Soft Constraints • Re-evaluates objective functions based on simulation results
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• In Builder: •
Tools CMOST Master Dataset Creator
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Oil Rate
Gas Rate
Water Rate
BHP
Oil Rate Parameter Matrix Perm, md Matrix Porosity Propped Frac Perm, md SW Propped Frac SW Nat Frac Rock Compaction
Water Rate
Original Model 0.0006 0.057 18,000 0.36 0.25 ctype4.inc
Best HM’d Gas Rate Model 0.000639 0.0529 14,195 0.358 0.385 ctype4.inc
Using CMOST we can d ifferenti ate between a frac’d well with “ planar” g eometry versus one with “ complex” geometry.
BHP
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