Reservoir Modeling and RTA of Multiply Fractured Horizontal WellsDealing with Non-Uniqueness in Reservoir Models of Shale Wells& Lessons in Humility

1. Reservoir Modeling and RTA of
Multiply Fractured Horizontal Wells
Dealing with Non-Uniqueness in Reservoir Models of Shale Wells
& Lessons in Humility
Narayan Nair
Linn Energy

2. Rationale
• Needed for improving capital efficiency – well
placement, frac sizing & spacing.
• To assess the risks due to the uncertainty in
the assumptions used in a reservoir model.
What if:
1. Matrix perm is lower/higher,
2. Half lengths are shorter/longer,
3. Number of producing fracs are different than assumed,
4. Degradation functions – relperm, PVT, geomechanics, are unclear.
• Interdependencies are clear.
• Narrow the uncertainty over time with more
wells:
1. Reduce a posteriori adjustments
2. Consensus – decision support.
2

3. Approach
OHIP
• Define fraccable net pay, porosity, Sw, etc.
• Easier to treat fraccable net pay uncertainty as different scenarios.
WPA
• What flow regimes are evident in the data?
• A viable model will have to fit the interpretation.
Testing
• Test interpretation under simplified SRV assumptions.
• More complicated characterizations can be converted to a simple model.
Uncertainty
Analysis
• Purpose of this presentation.
• Can be further constrained by play-wide analysis.
Add
Complexity
• Incrementally add complexities not considered in the simple model.
• Sensitivity to PVT, relperm, geomechanics.
Risk
Analysis
• Interdependencies are established.
• Range of possibilities (if needed stochastically) can be obtained.
3

4. What Do We Really Know?
• WPA relies on the industry legacy of 1D diffusivity equation = mass
balance + Darcy’s law.
• Linear flow in fractured well has been around a while in tight gas
reservoirs.
• Paradigm/coordinate shift with onset of shale wells. But, my
textbooks have “r” and “kh.”
• Extensive industry evaluation: sure “looks” like linear flow; and
several wells stay in transient flow for a long time.
4
Flow Regimes – Uncertainty Expressed in Lumped Parameters
Flow Regime “Types”
Known Parameters
“Skin” SRV Properties SRV Dimensions
Well is in Linear (Transient) Flow Rcomp Af√k Minimum HSR
Well performance in Linear Flow and
Transitions to Intra-Frac Interference Rcomp Af√k HSR
Flow regime seen predominantly in
Depletion
Range
Rcomp
Range
Af√k HSR

5. Ls -Frac Spacing
Perforated
Lateral
Length
SRV
Length
hf - Thickness
2Xf
Simplistic 1-D Representation
• SRV - Stimulated Reservoir
Volume
• XRV – External Drainage Volume
5
XRV
SRV
2f
fracs
A Lh 
 2 2f f f fA x h n    

6. WPA – Flow Regimes
• Wells in linear flow ‒ notice a high
rate.v.time b-factor fit.
• Time of transition ‒ Onset of
pseudosteady flow due to pressure
interference between fracs.
• Key question: for a well in linear flow,
can we predict it?
1
fA k
slope

2
transition
s
SR f transition
L
t
k
H A k t

 
6
1.00
10.00
100.00
1,000.00
0.1 1 10 100
GasRate,MscfD
Producing Time, years
½ Slope
Unit Slope
Transition Time
Shape factor

7. Building on the Conceptual Framework
• Reality is complex ‒
“assume the appearance of
without the reality.”
0.01
0.1
1
10
100
1000
0.1 1 10 100 1000 10000
Time (d)
InverseProductivityIndex,
(psi.d/Mscf)
Unit Slope
Half Slope
Half Slope
Linear flow –
complexity + branch
PSS – complexity
scale
Linear flow –
branch system
7

8. Limitations to WPA ‒ Why Test Interpretations?
• Formulation is based on single-phase flow.
– It is possible to adapt and understand the equivalent single-phase flow
answer to a liquid-rich reservoir; at least as a first guess.
– Use early-time flowback data!
• Pressure profiles at the frac face are extremely non-linear – the
pseudotime trick to linearize the 1D diffusivity equation is not
perfect.
– Square-root-time plot works best at constant pressure and ignores the
non-linearity in pressure.
– Superposition time function may not work in early-time data at a daily
data resolution.
– Restricted-rate wells may behave more as a constant rate solution.
• The solution to the equations assume infinite-acting fracture
conductivity.
– However, log-log plot is good at diagnosing finite conductivity effects.
• The conversion from a transition time to HSR is inexact.
8

9. Example Gas Well
Initial OGR
9

10. Well Performance Analysis ‒ Interpretation
• Interpretations:
– Well is in linear flow
– Productivity drop due to increased
drawdown, confirmed by a
decrease in condensate-gas-ratio.
– Hypothesis: Change in A√k
caused by increased liquid fallout
in the reservoir
10

11. Uncertainty Analysis
Assumptions:
• Max no. of fracs, nfmax = 80
• Min no. of fracs, nfmin = 40
• Max SRV dimension = 150 acres
1
10
100
1000
1 10 100 1,000
FractureSpacing,ft
Af,MMft2
Perm, nd
fA k
,minSRG
,minSRG
,maxSRG
fA k
,maxSRG
A√k , ft2√md 40,000
Perforated Lateral Length, ft Ll 6480
Number of clusters nc 80
Fraccable pay, ft h 100
Porosity 7%
Sw 40%
~75 acres 150 acres
nf= 40
nf= 80
1
2
3
4
11

12. High Perm – Min HSR
• nf = 40
• Frac spacing Ls = 166 ft
• Objective function → k, xf
• Calibration & model at the
cusp of transition
1
10
100
1000
1 10 100 1,000
FractureSpacing,ft
Af,MMft2
Perm, nd
fA k
,minSRG
nf= 40
nf= 80
1
• k = 100 nd
• xf = 250 ft
• Min-SRV ≈ 76 acres
12

13. What is a Calibration?
• The model obeys the
flow regime interpreted in
the WPA.
• The model reproduces
the degradation due to
liquid fallout in the
reservoir
• An adequate calibration
to the texture of the GOR
was not obtained
– PVT characterization is
not robust.
– Sensitivity to critical
condensate saturation
will help.
Synthetic model results imported into WPA
Example Well
13

14. Lower Perm – Min HSR
• nf = 80
• Frac spacing Ls = 82 ft
• We know k/Ls^2
– First guess k = 25 nd
• Calibration & model at the
cusp of transition
1
10
100
1000
1 10 100 1,000
FractureSpacing,ft
Af,MMft2
Perm, nd
fA k
,minSRG
nf= 40
nf= 80
2
• k = 25 nd
• xf = 250 ft
• Min-SRV ≈ 76 acres
14

15. Higher Perm – High HSR
• k = 25 nd
• xf = 485 ft
• Min-SRV ≈ 150 acres
1
10
100
1000
1 10 100 1,000
FractureSpacing,ft
Af,MMft2
Perm, nd
fA k
nf= 40
nf= 80
3
,maxSRG
• nf = 40
• Frac spacing Ls = 166 ft
• We know k/Ls^2
– First guess k = 25 nd
• Calibration & model should
not be close to transition
2
transition
s
i
SR f transition
L
t
k
H A k t

 
15

16. Low Perm – High HSR
• k = 7 nd
• xf = 485 ft
• Min-SRV ≈ 150 acres
• nf = 80
• Frac spacing Ls = 82 ft
• We know k/Ls^2
– First guess k = 7 nd
• Calibration & model should
not be close to transition
1
10
100
1000
1 10 100 1,000
FractureSpacing,ft
Af,MMft2
Perm, nd
fA k
nf= 40
nf= 80
4
,maxSRG
16

17. Well Analysis Synopsis 17
1
10
100
1000
1 10 100 1,000
FractureSpacing,ft
Af,MMft2
Perm, nd
fA k
,minSRG,maxSRG
nf= 40
nf= 80
1
2
3
4
1
2
3
4
Stochastic forecasts are possible at this
point:
• Randomly sample Ls,
• Sample k within the Ls.k box,
• Calculate Af from A√k,
• All data required for a simple model is
available with these three parameters.

18. Forecast Sensitivity
Under identical OHIP assumption:
Expect probabilistic forecasts to be constrained
with the ranges shown above.
HSR has a bigger effect on ultimate recovery
MM$? ‒ Can we continue removing liquids and
maintain drawdown?
Low Perm
Min HSR
High Perm
High HSR
Low Perm
High HSR
High Perm
Min HSR
18
Well spacing -1500 ft

19. Recognizing a Dynamic System
Known unknowns:
• Well interference
• Drawdown
• PVT – initial fluid in
reservoir, condensation,
& exsolution effects
• Relative Perm
– Example converted to a
wet gas PVT, with no
condensate dropout in
the reservoir.
• Reduction in fracture
effectiveness
• Stress (Pressure)
dependent matrix perm
19
A√k = 50,000
+25%

20. Well Interference
Bottom-line – Account for
non-volumetric effects.
• Create IP and EUR
expectation-reduction-
factor (if any) for down-
spaced wells.
• Relate this ERF to timing
of down-spacing in case
there is an existing
producing offset well.
• And, production impact
seen in producing offset.
• Can any detailed model
predict these effects?
20
SPE 162843
P50
EUR
Linear Flow Productivity Index
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF
Normalized Linear Flow Productivity Index
Spacing Test Control WellsATCE 2015

21. Reduction in Fracture Effectiveness
• Big question is does it affect Af or
conductivity of the fracture system?
– Large dataset study rarely showed finite
conductivity effects.
• Can we argue over small vs. large orders
of infinity?
21

22. Stress (Pressure) Dependent Perm
• This is a future concern only if PDP effects are not yet substantial in
the life of the well.
• If you are in a stress-dependent environment:
– Reasonable corrections are available in WPA to ensure unbiased flow-regime
interpretations.
– increased relperm reduction with decrease in saturation of initial phase could be
a good proxy for PDP effects.
• In Shale wells, CVD/DLE tests are a decent proxy for pressure-dependent saturation changes; you
could a priori merge stress/pressure dependence into relperm.
22
0
100
200
300
400
500
600
700
800
900
0 20 40 60 80 100 120
NormalizedPressure,psi.D/Mscf
Square Root Time, d^.5
0
50
100
150
200
250
300
350
400
450
500
0 20 40 60 80 100 120
STF**, d^.5
*Revised pseudopressure
**Revised pseudotime
definitions include PDP

23. Key Takeaways
• WPA leads to an interpretation that needs to be tested
using modeling.
• Calibrated models should obey WPA and continued
surveillance. Presence of phenomena can be
investigated by forward modeling and comparing
synthetic model WPA against well performance.
• Non-uniqueness is not unconstrained; in fact it can be
represented in a feasible range of explanations.
• Uncertainty in the key subsurface parameters will
reduce over time with continued surveillance &
playwide analysis.
• Opinion ‒ Probabilistic forecasts treating uncertainty in
static parameters, while ignoring dynamic phenomena,
do not adequately capture risk.
23

24. THANK YOU
Narayan Nair
Reservoir Engineer
14000 Quail Springs Pkwy., Ste 5000
Oklahoma City, OK 73134
T: 405.241.2258
nnair@linnenergy.com
24

25. APPENDIX
25

26. Reservoir Simulation Sensor (Engine) Coatsengineering.com
Pre- Post- Processor SANTEC Santecpe.com
RTA Harmony IHS/Fekete
Well Performance Analysis Crossbow Promethean.biz
PVT PVTSim Calsep.com
Frac Simulation M-Frac Baker Hughes
26
Toolkit

27. SRV Flow Regimes
– SRV: Linear transient flow
After wellbore/fracture storage and cleanup.
Pressure drainage away from the stimulated frac
surface face (Af ).
– SRV: Depletion
Characterized by quasi-steady depletion of SRV. The
transition from transient to depletion happens when
pressures interfere between the fracs.
27
f
n g ti
lt
gi gi
R c
J
B
A k



transition gi ti
SR lt transiti
s
on
STF c
G J ST
k
F
L

 

28. Example – Well in Linear Transient
Flow
Half Slope
28

29. Example – Well in Linear Transient Flow
Jlt
1
ltJ
slope

y-intercept
Rcomp
Straight-line
indicative of
linear flow
Based on
derivative: flat
during linear flow
Minimum
STFtransition
29

30. Example – Transition Occurred
Unit Slope
Half Slope
30

31. Example – Transition Occurred
STFtransition
Linear flow
1
ltJ
slope

Upward
curvature
Depletion
31

32. Uniform Fracture Spacing with Frac Complexity
SRV
wellbore

33. Uniform Fracture Spacing with Frac Complexity
0
100
200
300
400
500
600
700
800
0 500 1000 1500
Superposition Time Function (d^0.5)
InverseProductivityIndex
(psi.d/Mscf)
0
2.5
5
7.5
10
ApparentJlt(Mscf/psi/d^.5)
Jinv Jinv Fit Apparent Jlt
Immediate
transition or
frac
interference

34. Natural Frac/Fault Through System
34

35. Problem Statement for WPA
2X IP30
35

36. Flow Regime Identification
0.01
0.1
1
10
100
1 10 100 1000 10000 100000
Mscf/psi/D
Time, days
Inverse Productivity Index
Derivative Function of Inverse Productivity Index
I. SRV – Linear
Transient Flow:
Half-slope or
smaller
II. SRV –
Depletion: ~
Unit Slope
III. XRV – Linear
Transient:
Inverse PI is half-
slope or smaller
IV. XRV –
Depletion:
Concave &
higher than
unit slope
Constant pressure condition 36

37. Linear Flow Plot
0
2
4
6
8
10
12
14
0 5 10 15 20 25 30
STF (d^0.5)
InverseProductivityIndex(psi.d/Mscf)
Litke 1H Litke 31H
Litke 32H Litke 8H
Litke 7H Spotts Unit 2H
Kensinger Unit 2H Faulk Unit 3H
Patterson Unit 1H
Slope of line on this plot is inversely
proportional to a
Linear flow productivity index
37

38. Diagnosing Degradation
• Example quantifying the impact of interwell
interference
Frac hit
~Half Slope
Frac hit
38

39. Diagnosing Improvement
• Reservoir
processes tend to
be “smooth,”
while abrupt
changes can be
attributed to fracs.
1
fA k
slope

39

40. Predictive Reliability of Flowback Data 40
• Large control group of
50+ Hz wells to
compare flowback data
results against daily
data. Results:
– Qualitatively and
quantitatively precise
– Percent difference in
data that meets
discretionary criteria:
15% (should be the
same in a perfect world)
– Best Practice
Reminders:
• Use flow-back as a
guide in modeling
daily data
• Honor the data
holistically
Superposition Time Plot

41. Diagnosing non-Reservoir Pressure Losses 41

42. RTA Plots
Before
cleanout
After
cleanout
42

43. Estimating Initial Reservoir Pressure 43

44. Condensate Dropout
10
100
1000
100
1,000
10,000
0 5 10 15 20 25
ChokeSize,1/64inch
GasMscf/D,WaterBbl/D,
CasingPressurepsia
Days
44

45. Normalized Yield – Decay 45
100+ bbl/MMscf
Initial Yield
𝑂𝐺𝑅
𝑂𝐺𝑅 𝑚𝑎𝑥
0
0.2
0.4
0.6
0.8
1
1.2
0 20 40 60 80 100DimensionlessYeild
30 120 180 500 1000 Best Fit
Model vs. Reality
Shallow decline
Wet gas
Using long-term public data to understand change in OGR over time.
Then, calibrating EOS generated PVT and relperm to the OGR decay.

46. • sob overburden stress:
• Where,
• se is the effective stress exerted on
rock matrix, and
• p is the fluid pressure.
• Overburden stress remains the same (we think?).
• As you reduce fluid pressure by producing the
reservoir, the effective stresses act at the grain-to-grain
contacts to help support the lithostatic pressure
increases.
• The result of increased effective stress is to weaken
the overpressured rock.
• Laboratory evidence1 has shown that the effective
permeability of rock is reduced by increasing stress.
• The reduction in permeability due to reducing fluid
pressures in the reservoir is referred to as pressure
dependent permeability (PDP).
Overpressured reservoirs1
46
Bottomhole Pressure
Depth,ft
Lithostatic Pressure
~1 psi/ft
Hydrostatic
Pressure
~0.465 psi/ft
Overpressured
Region
ob e ps s 
Effective Stress
1 Poston and Berg (1997), Overpressured Gas Reservoirs.

47. Rk is a capillary model for permeability reduction
factor expressed as a function of reservoir pressure2:
 sob is overburden stress = lithostatic pressure
gradient × depth
 a is a PDP exponent or material coefficient3:
 Increasing a → More PDP
– a = 0 means constant perm in scenario A.
– a = 1.1 is the perm reduction function; scenario B.
PDP effects have been included in the linear flow
diagnostic plots by including the permeability
reduction factor Rk in the definitions of
pseudopressure and pseudotime4.
In the predictive model, the non linear form of the
diffusivity equation is solved using numerical
methods.
47
PDP formulation
 
  ob i
k
i ob
k p p
R p
k p
a
s
s
 
   
 
 
     0
t
k
p i gi ti
g t
R t dt
t c
t t c t
 
 
 
% %
% % %
 
   
i
wf
p
k
wf i gi gi
g gp
R p dp
p B
B p p
 

  
% %
% %
2. Modified pseudopressure definition to
include PDP
3. Modified pseudotime with PDP function
1. Reduction in permeability due to
increasing overburden stresses
2 Dobrynin (1970), Deformation and change in physical properties of Oil and Gas Collectors.
3 Friedel (2004), Numerical simulation of production from tight-gas reservoirs by advanced stimulation technologies.
4 Thompson et al. (2010), Modeling well performance data from overpressured shale gas reservoirs.

48. References
• PVT characterization − Whitson and Sunjerga
(2012), SPE 155499
• Okouma et. al. (2012), SPE 162843
• Nair & Miller, SPE 166468
• Warpinski et. al., 2005
• Dr. Mark Miller
48