Evaluation of Tight Gas Reservoirs Victor Hein, P.E. Ryder Scott Company June 14, 2009
Resource Pyramid
Large Volumes
t n e 1000 md Small Volumes High d y m n g p Quality o a l o l m o e 100 md e n v e D h D Medium 1 md d c e d e T Quality n s a a r e e g 0.1 md r t t n c e i l n l I B i r Tight D 0.001 md d Gas e u n i t Gas Coalbed Low n o Shales Methane Quality 0.0001 md C
Holdit Hol ditch ch et al
Resource Pyramid
Large Volumes
t n e 1000 md Small Volumes High d y m n g p Quality o a l o l m o e 100 md e n v e D h D Medium 1 md d c e d e T Quality n s a a r e e g 0.1 md r t t n c e i l n l I B i r Tight D 0.001 md d Gas e u n i t Gas Coalbed Low n o Shales Methane Quality 0.0001 md C
Holdit Hol ditch ch et al
Gas Consumption North America
Gas Consumption World
U. S. Net Natural Gas Imports
OECD Countries
Australia Austria Belgium Canada Czech Republic Denmark Finland France Germany Greece Hungary Iceland Ireland Italy Japan Korea Luxembourg Mexico Netherlands New Zealand Norway Poland Portugal Slovak Republic Spain Sweden Switzerland Turkey United Kingdom United States
World Gas Reserves
¾
Excludes Russia
Overview of World Gas Reserves
Significant Gas Facts • Tight Gas ± 20% of US Production • Unconventional Gas ± 44% of 2005 US Production • Unconventional Gas ± 49% of 2030 US Production • 2005 OECD ± 38 % World’s Gas Production • 2005 OECD ± 50 % World’s Gas Consumption • 2030 OECD ± 27 % World’s Gas Production • 2030 OECD ± 42 % World’s Gas Consumption
Tight Gas Resource Triangle • 58 TCF produced through 2000 • 34 TCF Proven Reserves in 2001 • Technically Recoverable volume 185 TCF • Undiscovered 350 TCF • Additional GIP 5000 TCF
Source GTI 2001
Tight Gas Characteristics • Low Permeability (<0.1md) • Frac Job or Horizontal Well Required • Large Pressure Gradients across Reservoir • High Transient Decline Rates • Often Commingled Production • Often Layered and Complex
Evaluation Methods
• Volumetrics • Material Balance • Decline Curves • Production History Matching • Advanced Production Analysis • Simulation
Volumetrics
Archie Equations Clean Sand
For low porosity sandstones: a is typically 1.0 m initially thought to be 2.0, later used values of 1.8-2.0 for tight gas
Shaley Sand
• Fertl and Hammack reduction of Simandoux • Original Simandoux (widely used) based on very limited samples • Vsh is effective shale volume, fraction • F is from shale corrected porosity • Rsh is the resistivity of the shale in sand – recommends 0.4R of shale beds
Hilchie 1982 Advanced Well Log Interpretation
Density Porosity Corrections for Invasion Clean Sand
• Density gets most of response from 3-4” from wellbore • Solve equations by trial and error • Initial guess for ρmf is from ρmf = 1 + 0.73P where P is Salinity in ppm divided by 1,000,000 • Calculate gas density or estimate from following figure • When numbers converge you have answer Hilchie 1982 Advanced Well Log Interpretation
Density Porosity Gas Density
Hilchie 1982 Advanced Well Log Interpretation
Density Neutron Porosity Type I Invasion Profile
• Very deep or very shallow invasion - logs read same fluid • Quick approach below, best simultaneous eq using Rxo
Hilchie 1982 Advanced Well Log Interpretation
Density Neutron Porosity Type II Invasion Profile
•
Invasion on order of 3-4” but not beyond neutron
•
Simultaneous equations for density with Rxo device – best
•
Use density porosity only – will be somewhat high Hilchie 1982 Advanced Well Log Interpretation
Combined Archie Equation Clean Sand
Pickett Plot Example
Their New Procedure
¾
R1(T1+6.77) = R2(T2+6.77)
Conclusions
Conclusions
What Is Pay?
0.5 Bscf Well
2.0 Bscf Well
High Resolution in Layered Sands
Net pay added using high resolution is 50 feet!
Net pay 18ft
Net Pay • Low Permeability Zones Often Have Extensive Transition Zones • Calibrate Cutoffs with Cores • Archie Equation Breaks Down at Very Low Porosities for m = 2 • Watch Out for Laminated Sands Below Vertical Resolution of Logs
Data Integration
General Observations Log Analysis • Tight gas systems often contain layered and/or dispersed clay (analysis methods different) • Core data and FMI often critical to understanding type system and existence of fractures • Must depth shift logs particularly in layered system • Calibrate logs and k estimates to cores • Consider special core analysis in new plays • Full logging suite required for shaley sands
General Observations Log Analysis • Rw often difficult to obtain or estimate • Pickett plot can tend to overestimate Rw and SW • Shale models are complex may not yield correct answers • MRI can help with porosity, k, free water (Hamada et al SPE 114254, SPE 90740, Coates –1999, Prammer et al - 1996)
• Using Density and NMR porosities together can improve porosity estimates (Hamada et al SPE 114254) • Rock typing very important (Rushing et al SPE 114164) • Porosity determination difficult due to matrix changes, incomplete invasion, and clay (Kukal et al SPE 11620)
• GR generally better Vsh tool than D-N XP in older compacted rocks (Kukal et al SPE 11620)
What Is Effective Drainage Area?
0.1 md
0.001 md
1 Year
0.01 md
0.0001 md
0.1 md
0.001 md
10 Years
0.01 md
0.0001 md
Effective Drainage Area • Drainage Area f(k, Xf , Porosity, Geometry) • Have Dependent Relationship Between Effective Drainage Area and Recovery Factor • Should Define Effective Drainage Area Relative to Time and Recovery Factor
Core Analysis • Analysis critical to understanding of layered or complex reservoir • Must measure rock properties under NOB (Jones and Owens, Soeder and Randolf)
• Can have ten fold or more reduction in permeability due to NOB at 0.01 md and below • Lower permeability rocks - smaller pore throats
CER, Holditch & Assoc 1991
Reduction of k with net overburden
CER, Holditch & Assoc 1991
Reduction of k with net overburden Mesaverde Formation
Estimation of Permeability From Logs Example – Timur’s Equation m
k =
K aφ S wi
c
• c = 2 since k inversely proportional to surface area squared and Swi proportional to surface area • Plot
φ
2 vs k ( S wi ) - straight line with slope m on log log
plot and y axis intercept at K a m related to tortuosity of the rock
Kukal, Simons SPE 13880
Estimation of k in very tight rocks • • • •
Timur’s: little data < 1 md, also unstressed k Predicted k two orders of magnitude high for 0.1µd < k < 0.1md Clay increases tortuosity, surface area Better method: plot k(Swi**2) vs. (Φ(1-Vcl) on log log plot
•
where: Swi and Vcl in fractions
•
K includes effect of overburden at 1.0 psi/ft
•
Swi must be at irreducible
•
must correct k to Kg
•
Derived from Mesaverde core date in Western Colorado Kukal, Simons SPE 13880 ** means to the power of
Estimating k where Swi unknown • Plot k vs. (Φ(1-Vcl)) on log log plot
k = 171.4(φ (1 − V cl ))
3.86
• Porosity and Vcl in fractions • Only slightly less accurate that equation with Swi • Derived from Mesaverde also works in Travis Peak in East Texas • Other examples of “slot pore geometry” are Alberta’s deep Spirit River, East Texas Cotton Valley, Piceance Cozzette, Wyoming • Should be useful in many low k sandstones Kukal, Simons SPE 13880
Material Balance P/Z
P/Z Based on Tank Model • Constant Volume • No Efflux or Influx • Pressure Gradients Small • Measured Pressures Representative of Average Pressure
Tight Gas P/Z Plot
Radius of Drainage –Radial Flow
Transient vs. Boundary Flow Constant Rate Example 4000
3500
Cross Section
3000
Transient Well Performance f(k, skin, time) 2500
Boundary Dominated Well Performance f(Volume, PI)
2000
Plan View
Fekete RTA Documentation
Transient vs. Boundary Flow Transient Flow • Early time or low permeability. • Flow that occurs when the pressure “pulse” is moving into an infinite or semi infinite acting reservoir. • The “fingerprint” of the reservoir. Contains information about reservoir properties ie k
Boundary Flow • Late time flow behavior. • Typically dominates long term production data. • Reservoir is in a state of pseudo-equilibrium –mass balance. • Contains information about reservoir pore volume (OGIP).
Fekete RTA Documentation
Time to Pseudo Radial Flow
t D X f =
0.006328kt
φμ ct x f
2
≅3
Lee, Wattenbarger SPE Textbook 5
Duration of Flow Periods – HF Well
•
Lf (ft)
k
100
1
100
telf
(md)
tsprf
0.3 hrs
51.2 hrs
0.01
27.3 hrs
213 days
1,000
0.01
114 days
58 years
100
0.001
11.4 days
5.8 years
1,000
0.001
3.1 years
No way!!
Ф = 0.15, CrD = 100, μ = 0.03 cp, ct = 0.0001 1/psi •
telf is time to end of linear flow
•
tsprf is time to start of pseudo radial flow
•
Lf is half frac length
•
times assume no interference from boundaries
Tight Gas Pressure Buildup Tests • very important to run prefrac BU for k and P wsi • prefrac results can insure on proper straight line after production period of significant length for pseudo radial • common problem in PT tests is that shut in period is too short • too short of flow period can also be a problem i.e wellbore unloading is incomplete (mass rate at surface exceeds mass rate out perforations) • consider bottom hole shut-in (tubing plug) if afterflow exceeds maximum practical test time
Pressure Buildup Test Design • make estimates of kg from guess then test data • estimate end of WBS • estimate beginning of pseudo radial flow • estimate onset of BDF • post frac estimates for time use type curves
SPE 17088, Dr. W. J. Lee
Static Material Balance Problems • Difficult to Analyze Due to Required SI Time, Heterogeneity, Large Pressure Gradients • Common Curved Behavior • Can Result in Large Errors for GIP which are Generally Low for Early Cum Values • Increased SI Times Help but GIP Generally Low • Scatter = f(Pressure Gradients, Heterogeneity)
Static Material Balance Summary • Get Pre Frac Initial Pressure • Use Longer SI Times if Possible • Existence of Straight Line Does Not Insure Tank Behavior • If Curved or Two Slopes Look at Later Straight Line • If Possible, QC Shut-in Times
Illustration of Pseudo Steady State
p1 1
p 2
2 e r u s s e r p
3
pwf1 pwf2
p 3 time
Constant Rate q pwf3
r w
Distance
r e Fekete
Flowing p/z Method for Gas – Constant Rate - Mattar L., McNeil, R., "The 'Flowing' Gas Material Balance", JCPT, Volume 37 #2, 1998
pi zi
Pressure loss due to flow in reservoir (Darcy’s Law) is constant with time
pwf
⎛ p ⎞ = ⎜ ⎟ + constant z ⎝ z ⎠ wf p
zwf
Gi
Measured at well during flow
G p
Flowing p/z Method for Gas – Variable Rate
pi zi
Pressure loss due to flow in reservoir is NOT constant
pwf
⎛ p ⎞ = ⎜ ⎟ + qb pss z ⎝ z ⎠ wf p
zwf
Unknown
Gi Measured at well during flow
G p Fekete
Variable Rate p/z – Procedure (1) Unnamed Well
Flowing Material Balance Legend Static P/Z* P/Z Line Flowing Pressure
550
500
450
Step 1: Estimate OGIP and plot a straight line from pi/zi to OGIP. Include flowing pressures (p/z)wf on plot
400 F
l 350 o
300
250
w i n g P r e s s u r e , p s i
200
150
100
50
Original Gas In Place
0 .00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 Cumulative Production, Bscf
Fekete
Variable Rate p/z – Procedure (2) Unnamed Well
Flowing Material Balance Legend
550 Static P/Z* P/Z Line Flowing Pressure 500 Productivity Index
4.40
4.00
3.60 ) P c / 2 3.20 i s p 6 0 1 ( / 2.80 d f c s M M2.40 , x e d n I y 2.00 t i v i t c u d 1.60 o r P
Step 2: Calculate bpss for each production point using the following formula:
b pss =
⎛ p ⎞ ⎛ p⎞ − ⎜ z ⎟ ⎜z⎟ ⎝ ⎠line ⎝ ⎠wf
450
400 F
l 350 o
300
q
250
Plot 1/bpss as a function of Gp
200
1.20
150
0.80
100
0.40
50
Original Gas In Place
0.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70
0
Cumulative Production, Bscf
Fekete
w i n g P r e s s u r e , p s i
Variable Rate p/z – Procedure (3) Unnamed Well
Flowing Material Balance Legend
550 Static P/Z* P/Z Line Flowing Pressure 500 Productivity Index
4.40
4.00
3.60 ) P c / 2 3.20 i s p 6 0 1 ( / 2.80 d f c s M M2.40 , x e d n I y 2.00 t i v i t c u d 1.60 o r P
Step 3: 1/bpss should tend towards a flat line. Iterate on OGIP estimates until this happens
450
400
350
300
250
F l o w i n g P r e s s u r e , p s i
200
1.20
150
0.80
100
50 Original Gas In Place
0.40
0.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70
0
Cumulative Production, Bscf
Fekete
Variable Rate p/z – Procedure (4) Unnamed Well
Flowing Material Balance Legend
550 Static P/Z* P/Z Line Flowing P/Z* 500 Flowing Pressure Productivity Index
4.40
4.00
3.60 ) P c / 2 i 3.20 s p 6 0 1 ( / 2.80 d f c s M M2.40 , x e d n I y 2.00 t i v i t c u d 1.60 o r P
Step 4: Plot p/z points on the p/z line using the following formula:
⎛ p ⎞
⎜ z ⎟ ⎝ ⎠ data
⎛ p⎞
= ⎜ ⎟ + qb pss ⎝ z ⎠ wf
“Fine tune” the OGIP estimate”
450
400
350
300
250
200
1.20
150
0.80
100
0.40
1/bpss
50 Original Gas In Place
0.00 0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 Cumulative Production, Bscf
Fekete
P / Z ,* F l o w i n g P r e s s u r e , p s i
Flowing Material Balance • FTP converted to FBHP • Pseudo Pressure and Pseudo Time to Correct for Viscosity and Compressibility Changes • Uses BDF flow equation for Gas simplified to
q
Δ p p
=
1 b pss
Giα
G pa
Δ p p
+
1 b pss
• Iterative Process Dependent on guess for OGIP • Plot Normalized Rate and Cum Prod
Flowing Material Balance
q Δ p p
G pa
Δ p p Fekete
Estimate for bpss
Fekete
Flowing Material Balance • Curve is concave up until PSS - generally yielding minimum OGIP • Model is well in Center of Circle • Liquid Loading, Condensate Ring, Scale, etc. can Affect Results • Don’t use where Water Drive or Abnormal Pressure • Use with Caution for High Perm Variations • Can be Useful but be Careful
Decline Curves
Decline Curve Equations - Arps Exponential
Hyperbolic
The Hyperbolic Decline Curve Rate vs. Cumulative Prod.
Unnamed Well 4.50
4.00
q=
3.50
qi
(1 + bDit )
1 / b
Hyperbolic Decline: 1.Decline rate is not constant D=Kqb. 2.Straight line plots NOT practical and b is determined by nonlinear curve fit.
3.00 d f c s M2.50 M , e t a R s a 2.00 G
D =
1.50
1.00
0.50
D = f (t )
0.00 0.00 0.10 0.20 0.30 0.40 0.50
0.60 0.70 0.80 0.90 1.00 1.10
1.20 1.30 1.40 1.50 1.60 1.70
Di qi
1.80 1.90 2.00 2.10 2.20 2.30
b
q
b
2.40 2.50 2.60
Gas Cum. Prod., Bscf
Fekete
Arps Traditional Analysis • Based on Empirical Observations • Exponential (D is constant) • Hyperbolic (D changes with time, 0
Types of Decline Curves - Arps
Criteria for Arps Analysis • Well Produced at or near Capacity • Constant Flowing Bottom Hole Pressure • Drainage Area Remains Constant – Boundary Dominated Flow (BDF) has been achieved • Same Completion
What About b > 1 ? • Wrong Interpretation • Transient Flow instead of Boundary Dominated
Effects of b Factor
Cox, et al SPE 78695
Deep Tight Gas Example
0.0009 < k < 0.07 md Spacing 80 acres Pwsi = 16,200 psia BHT 400 deg F Xf = 300’ (unless specified) Porosity = 6.6% Fracture k = 100md Sw = 36% Kv/Kh = 0.001 Thickness = 200’ Rushing, et al SPE 109625
Effects of Layers on b Exponents Years
b
b
b
b
Error
Error
Error
Error
1 Lay
4 Lay
8 Lay
16Lay
(%)
(%)
(%)
(%)
1Layer 4Layer
8Layer 16Layer
1
3.62 2.78
2.89 2.97
132
110
117
128
5
2.95 1.35
1.30 1.39
58
22
11
20
10
1.48 1.04
1.18 1.26
19
8
9
11
20
0.58 1.01
1.04 0.96
0.1
7
7
3
Rushing, et al SPE 109625
Effects of Xf on b Exponents Years
b
b
b
b
Xf=50 Xf=100 Xf=300 Xf=500
Error
Error
Error
Error
(%)
(%)
(%)
(%)
Xf=50
Xf=100 Xf=300 Xf=500
1
4.01
3.60
2.78
1.91
145
139
110
78
5
1.53
1.44
1.35
1.20
34
25
22
12
10
1.10
1.08
1.04
1.03
14
10
8
7
20
1.07
1.06
1.01
0.96
11
9
7
6
Rushing, et al SPE 109625
Synthetic Single Reservoir 80 acres
Cheng, Lee, McVay SPE 108176
Synthetic Single Reservoir 80 acres
Cheng, Lee, McVay SPE 108176
Synthetic Single Reservoir 80 acres
Cheng, Lee, McVay SPE 108176
Synthetic Single Reservoir 80 acres all data included
• All predictions from regression are too high • All values of b >1.0 • b is proportional to D i • Percent error increases as b increases • Correct values for b cannot be directly obtained from transient data Cheng, Lee, McVay SPE 108176
Synthetic Single Reservoir 80 acres
•
Stabilization time was 4.4 years
•
Discarded all data prior to 5.0 years
•
b generally decreases with time and all b values < 1.0
•
Results indicate that using only stabilized data sufficiently accurate Cheng, Lee, McVay SPE 108176
Decline Curve Estimate Single Layer, b constrained to 1.0
Cheng, Lee, McVay SPE 108176
Decline Curve Estimate Single Layer, b constrained to 1.0
Cheng, Lee, McVay SPE 108176
Decline Curve Estimate Single Layer, b constrained to 1.0 • b= 1.0 results in either underestimates or overestimates • At early times production generally underestimated • Forecasts tend to be more stable as more late time data are included in the analysis
Cheng, Lee, McVay SPE 108176
Additional Observations • b for stabilized flow related to reservoir drive mechanism, fluid properties and reservoir conditions Fetkovich et al 1996, Chen and Teufel 2002
• b decreases as reservoir depletes • Average b during entire depletion phase (BDF) will be < 1 Chen and Teufel 2002
Cheng, Lee, McVay SPE 108176
Improved Analysis Technique
Calculate bE • Pi = initial reservoir pressure • Pp,n = is normalized pseudo pressure • Cgi is isothermal compressibility @ Pi • Zi evaluated at Pp, Zwf evaluated at Pwf Chen 2002
Improved Analysis Technique
Cheng, Lee, McVay SPE 108176
Improved Analysis Technique
• Back extrapolate to get qi at zero delta time Cheng, Lee, McVay SPE 108176
Improved Analysis Technique
• Back extrapolate to get Di at zero delta time Cheng, Lee, McVay SPE 108176
Improved Analysis Technique
Cheng, Lee, McVay SPE 108176
Improved Analysis Technique Multi Layer • Estimate b at 0.6 • No theoretical basis, based on observed results from a few field and synthetic cases • Other procedures are the same
Cheng, Lee, McVay SPE 108176
Decline Curve Analysis CBM Rushing, Perego, Blasingame studied CBM behavior using simulation (SPE 114514) • Long term b exponents ranged from 0.20 to 0.80 • Early decline behavior for many wells was exponential becoming more hyperbolic with time • None of the simulated cases exhibited long term exponential behavior due to non linear relationships between key coal properties and either pressure or saturation • Wells with higher Pwf (all other factors being equal) exhibited higher b values for long term production
Improved Decline Curve Analysis Additional method proposed by Ilk, Rushing, Perego, and Blasingame (SPE116731) • Presents power law lost ratio method • Presents diagnostic curves to aid in decline type - hyperbolic, exponential • Method has merit, however, industry probably slow to replace traditional decline curve methods
Summary Conventional Analysis • • • • • • •
Fit Hyperbolic in BDF region Research Time in Transient Flow! See if can Fit with b ≤ 1.0 using later prod data Never use b ≥ 1.0 for Last Segment in forecast Research Terminal Declines for Last segment Use Improved or Advanced Methods Analogies Should Have – – – –
Similar Completions Similar Reservoir Parameters Similar Spacing Sufficient Production History for Reliable Analysis
Type Curve Changes With Spacing 100,000
] f c M [ s a G
10,000
160 acre 80 acre 40 acre 1,000 0
20
40
60
Months
80
100
1 20
Production History Matching
Production History Matching
• Example PROMAT • Single-Phase, Single-Layer Analytical Model combined with Regression Analysis • Fast + Can Provide Accurate k, S (Xf ) and sometimes Drainage Area • Accuracy Good where k Variation not big (Sergio Vera, MS Thesis, Texas A&M 12/2006)
Production History Match Example
Production History Matching - Problems • Non-Unique Solutions without Good Reservoir Description • Pre-frac k can Over Estimate Reserves • Inaccurate in Layered Systems with Large Permeability Variations • Accuracy Increases with Production Data • Multi-Layer Models often Require Detailed Data such as Production Logs, etc.
Advanced Production Analysis
Flow Periods for Fractured Well
• Most of flow due to expansion in fracture • Generally too early to be of practical use • Often masked by WBS Cinco et al 1981
Flow Periods for Fractured Well
• Two types of linear flow simultaneously occur • Most of flow comes from formation • Cannot determine frac length just from bilinear flow • Plot of Pwf vs t**1/4 is straight line, plot of ΔP or Δm(p) vs time is ¼ slope on log log plot Cinco et al 1981 ** means to the power of
Flow Periods for Fractured Well
• Occurs only where high conductivity fracture, C r D ≥ 100 • Continues approx tLf D = 0.016 • Plot of Pwf vs. t**1/2 is straight line, plot of ΔP or Δm(p) vs time is ½ slope on log log plot Cinco et al 1981 ** means to the power of
Flow Periods for Fractured Well
• Transition period between linear flow and radial flow • Badazhkov et al (SPE 117023) contains method and references
Cinco et al 1981
Flow Periods for Fractured Well
• Fracture functions as extended wellbore consistent with effective wellbore radius concept • Large Lf compared to drainage area can mask due to BDF • Begins at tLf D of approx 3 for CrD ≥ 100, less for lower CrD • Pwf vs log t is straight line
Cinco et al 1981
Tight Gas Flow General Behavior ¾
• ¾
•
Small Xf compared to ROI Linear to Pseudo Radial –less common Large Xf compared to ROI Long Term Linear Flow followed by BDF
Infinite Acting Linear Systems •
Parallel Reservoir or No Flow Boundaries
Analysis of Linear Flow • Plot of (m(pi)-m(pwf ))/qg vs t**1/2 yields straight lines of different slopes • Slope departs from analytical value as flow rates or degree of drawdown become higher • Don’t see the same degree of departure from analytical solutions for pseudo radial flow
** means to the power of
Analysis of Linear Flow
Ibrahim and Wattenbarger SPE 100836
Analysis of Linear Flow
Ibrahim and Wattenbarger SPE 100836
Analysis of Linear Flow
Ibrahim and Wattenbarger SPE 100836
Analysis of Linear Flow
Ibrahim and Wattenbarger SPE 100836
Analysis of Linear Flow
Ibrahim and Wattenbarger SPE 100836
Analysis of Linear Flow
Ibrahim and Wattenbarger SPE 100836
Analysis of Linear Flow Flow Corrections to Constant Pwf case for Drawdown
• Define Dimensionless Drawdown as:
• Define correction factor as: • Solutions become
Ibrahim and Wattenbarger SPE 100836
Analysis of Linear Flow Corrections to Constant Pwf case for Drawdown
Ibrahim and Wattenbarger SPE 100836
Analysis of Linear Flow Synopsis
k Ac
from slope of (m(pi)–m(pwf ))/qg vs sqrt(t) plot
• Determine pore volume from slope and time to end of linear flow, OGIP by including rock and fluid properties • Cannot determine k independently without A c • Slope of sqrt(t) plot affected by drawdown for constant pwf case • Without correction factor can be in error by up to 22% at maximum drawdown • No correction factors yet available for constant rate Ibrahim and Wattenbarger case SPE 100836
Advanced Production Analysis • Combines Concepts from Pressure Transient Analysis with Production Data • Allows for Determination of k and S or Xf in Transient Region, OGIP from BDF • Newer Methods (Post Fetkovich) Allow Changes in Operating Conditions • Can also use for Diagnostic Analysis (Transient, BDF, Interference)
Fekete
Fetkovitch • Combination of Analytical Transient Model and Traditional Arps • Vertical Well, Center of Closed Circle, Single Phase Fluid • Requires Constant Flowing Bottom Hole Pressure - less useful for gas wells • Type Curve Match of Qd and Td against actual rate versus time
Definition of Material Balance Time (Blasingame et al) Actual Rate Decline
Equivalent Constant Rate
q Q
Q
actual time (t)
material balance = Q/q time (tc) Fekete
Constant Pressure and Constant Rate Solutions (Oil) Comparison of qD with 1/pD Cylindrical Reservoir with Vertical Well in Center 1000
100
Infinite Acting
Boundary Dominated
Constant Rate Solution 1/pD Harmonic
10
0.9
1
/ 1 d n a D q
0.1
Definition 0.01
q D = 0.001
0.0001
1 p D
=
141.2 q μ B kh( pi − pwf )
Constant Pressure Solution qD Exponential
0.00001
0.000001 0.000001
0.0001
0.01
1
100
10000
1000000
100000000
1E+10
1E+12
1E+14
tD
Fekete
Darcy’s Law Correction for Gas Reservoirs
Δ p ∝ q
Darcy’s Law states :
For Gas Flow, this is not true because viscosity ( ) and Z-factor (Z) vary with pressure
Solution: Pseudo-Pressure p
p p = 2
∫ 0
pdp
μ Z
Fekete
Depletion Correction for Gas Reservoirs: Pseudo-Time Solution: Pseudo-Time
t a = (μ cg )i
μ , c g
→
t
dt
0
g
∫ μ c
Evaluated at average reservoir pressure
Not to be confused with welltest pseudo- time which evaluates properties at well flowing pressure
Fekete
Material Balance Time -MBT is a superposition time function - MBT converts VARIABLE RATE data into an EQUIVALENT CONSTANT RATE solution. - MBT is RIGOROUS for the BOUNDARY DOMINATED flow regime - MBT generally works very well for transient data also, but is only an approximation (errors can be up to 20% for linear flow)
Fekete
Blasingame Type Curve Analysis Blasingame type curves have identical format to those of Fetkovich. However, there are three important differences in presentation: 1. Models are based on constant RATE solution instead of constant pressure 2. Exponential and Hyperbolic stems absent, only HARMONIC stem is plotted 3. Rate Integral and Rate Integral - Derivative type curves are used (simultaneous type curve match)
Data plotted on Blasingame type curves makes use of MODERN DECLINE ANALYSIS methods: - NORMALIZED RATE (q/ p) - MATERIAL BALANCE TIME / PSEUDO TIME
Fekete
Blasingame Type Curve Analysis- Comparison to Fetkovich
Fetkovich
Blasingame
log(q)
log(q/ p)
log(qDd)
log(qDd) log(t)
log(tDd)
log(tca)
log(tDd)
- Usage of q/Δp and tca allow boundary dominated flow to be represented by harmonic stem only, regardless of flowing conditions - Blasingame harmonic stem offers an ANALYTICAL fluids-in-place solution - Transient stems (not shown) are similar to Fetkovich Fekete
Blasingame Type Curve Analysis- Definitions Typecurves
Normalized Rate Rate Integral Rate Integral - Derivative
q Dd =
141.2qβμ ⎡ ⎛ r e ⎞ 1 ⎤ ⎢ln⎜ ⎟ − ⎥ khΔP ⎣ ⎝ r wa ⎠ 2 ⎦
q Ddi =
1 t DA
(t )dt
Dd
0
q Ddid = t DA
dq Ddi dt DA
Data - Gas q
ΔP p
ΔP t c
t DA
∫q
Data - Oil q
⎛ q ⎞ 1 q dt ⎜ ⎟ = ∫ ⎝ ΔP ⎠i t c 0 ΔP ⎛ q ⎞ ⎟ ΔP ⎠ i ⎛ q ⎞ ⎝ ⎜ ⎟ = t c dt c ⎝ ΔP ⎠id d ⎜
⎛ q ⎞ ⎜ ⎟ = 1 ⎜ ΔP p ⎟ t ca ⎝ ⎠i ⎛ q ⎞ ⎜ ⎟ = ⎜ ΔP p ⎟ ⎝ ⎠id
t ca
q
∫ ΔP
dt
p
0
⎛ q ⎞ ⎟ ⎜ ΔP p ⎟ ⎝ ⎠i
t ca d ⎜
dt ca
Fekete
Blasingame, et al Utilizes Flowing Pressures 3 Different Rate Functions can be Plotted against Time Function (Material Balance Time) • Normalized Rate q
Δ p p
• Rate Integral (ave rate to production time) • Rate Integral Derivative Material Balance Time make Solution look like Constant Rate, hence • Depletion Stem of Normalized Rate is Harmonic
Blasingame, et al Select Model •Radial •Infinite Conductivity Fracture •Finite Conductivity Fractures •Elliptical Flow •Horizontal Well Obtain match, multiple functions should fit same TC Possible to obtain k and S or X f Can obtain OGIP if in BDF
Blasingame, et al
Fekete
Advanced Production Analysis Blasingame and others • Tight gas reservoirs can suffer from non unique solutions • Must have good idea of OGIP to reduce the nonuniqueness problem • Even prefrac buildup for k and a post-frac buildup for Xf does not guarantee a unique solution • Can use decline curves or FMB to estimate OGIP
Important Type Curve Techniques • Palacio and Blasingame
(SPE 18799, Fekete RTA documentation)
• Agarwal, Gardner, et al (SPE 57916, Fekete RTA documentation)
Important Other Methods Crafton, Reciprocal Productivity Index
(SPE 37409, 49223)
Ozkan, et al Transient RPI for Horizontal Wells (SPE 77690, 110848)
Reservoir Simulation
Reservoir Simulation • Gold Standard for Evaluation • Expensive, Time and Data Intensive • Danger is Experience Level of “Hands On” Workers or Weakest Link • Simulation Requires Knowledge of General Reservoir Engineering and Production Engineering • Must have People in you Organization to Understand Work Process, Results and Integrate with Common Sense
Cox et al SPE 98035
r e Generally Proportional to Lf, k
Cox et al SPE 98035
r e Generally Proportional to Lf, k
Cox et al SPE 98035
Practical Limit Exists for Geometry and low k
Cox et al SPE 98035
Synopsis for Accurate Evaluation • Industry Acceptance and Time Constraints Require Mostly Traditional Decline Analysis • Volumetrics Must be Augmented with Core Data, Analogy, Information from More Advanced Methods or Insights from Performance particularly at Lower Permeability • Advanced methods are useful for obtaining: K, S, or Xf for Transient Flow OGIP for Boundary Dominated Flow and sometimes Linear Flow For OGIP, Confirm from Several Methods or with Reservoir Simulation or Analytical Model
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