A project to compile different methods in reserves estimation, namely Decline curve analysis, Material Balance, Rate transient Analysis, Series Model. Applied for unconventional resources in which the difference from the conventional has been revealed. Utilized KAPPA software thoroughly during the project.

1. DETERMINISTIC RESERVES ESTIMATION
Homework 9
Instructor: Dr. Shah Kabir
Group members:
Aakash Shah 1468484
An Tran 1596068
Joseph O Ojero 1595331
Marcio Farias de Araujo 1376978
Vishrut Chokshi 1536843

2. Objectives
 History match and compare production performance forecast
of unconventional oil reservoirs using various analytical models
 Methods used (Outline)
 Decline Curve methods
 Arps
 Modified Arps
 PLE
 Material Balance methods
 Transient PI
 Rate Transient Analysis
 Series Model
 Approach: Compare the total recovery after 3 years forecast
for each well and methods

3. Well 3 – Arps &
Modified Arps
10
100
1000
10000
1 10 100 1000 10000
Rate,STB/D
te, Days
Diagnostic Rate vs Time log-log plot
Transient flow
BDF
y = 1481.5e-0.003x
R² = 0.5571
10
100
1000
500
Rate,STB/D
Time, Days
BDF
y = 4895.2e-1E-05x
R² = 0.4904
10
110
210
310
410
230000 260000 290000
Rate,STB/D
Cumulative-prod. STB
Rate vs Cumm
BDF
Transient flow
Comparison
After 3 years performance forecast
- Arps’ DCA (b = 2) gives a total recovery of 0.393 MMSTB
- Modified Arps’ DCA gives a total recovery of 0.316 MMSTB

4. Methodology
Well 3 - PLE
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+08
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 Gp,MSCForNp,STB
qg,MSCF/dayor
qo,STB/day
Time, days
q and Gp or Np vs. Time, days
qo_wo_Dinf_STB/day_(PLE_qDb)
qo_w_Dinf_STB/day_(PLE_qDb)
qo_STB/day_edited
Np_wo_Dinf_MMSTB_(PLE_qDb)
Np_w_Dinf_MMSTB_(PLE_qDb)
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04
D-parameter
Time, days
D-parameter vs. Time, days
D_wo_Dinf
D_w_Dinf
D=1/q*dq/dt
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04
b-parameter
Time, days
b-parameter vs. Time, days
b_wo_Dinf
b_w_Dinf
b=d/dt*1/D
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04
Dandbparameters
qg,MSCF/dayor
qo,STB/day
Time, days
qDb vs. Time, days
• ‘b’ value should be a generally declining function.
• 4 variables
• n- time exponent: shape controlling factor

5. Methodology
Well 3 - PLE
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+08
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 Gp,MSCForNp,STB
qg,MSCF/dayor
qo,STB/day
Time, days
q and Gp or Np vs. Time, days
qo_wo_Dinf_STB/day_(PLE_qDb)
qo_w_Dinf_STB/day_(PLE_qDb)
qo_STB/day_edited
Np_wo_Dinf_MMSTB_(PLE_qDb)
Np_w_Dinf_MMSTB_(PLE_qDb)
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04
D-parameter
Time, days
D-parameter vs. Time, days
D_wo_Dinf
D_w_Dinf
D=1/q*dq/dt
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04
b-parameter
Time, days
b-parameter vs. Time, days
b_wo_Dinf
b_w_Dinf
b=d/dt*1/D
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04
Dandbparameters
qg,MSCF/dayor
qo,STB/day
Time, days
qDb vs. Time, days
• ‘b’ value should be a generally declining function.
• 4 variables
• n- time exponent: shape controlling factor
n = 0.052, Di^ = 5.6424 1/days, Dinf = 1.41E-03 1/days, qi^=812,662 STB/D
Comparison
After 3 years performance forecast
- EUR from PLE w/o Dinf: 0.59 MMSTB
- EUR from PLE with Dinf: 0.29 MMSTB

6. Methodology
Utilizing Excel Solver, change tf, tm and Tx/Jf until the minimum value
for S[(qdata-qmodel)2] for all data points is reached.
Well 3 - SERIES MODEL

7. Well 3 - SERIES MODEL
Production Forecast
tf = 0.00507 tm = 614.98
Tx/Jf = 0.1989
Recovery @ 3 yrs
0.373 MSTB

8. Well 3 - Comparison
 Well 3 Forecast
0
50000
100000
150000
200000
250000
300000
350000
400000
450000
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Np(STB)
Time (days)
Reserve Estimation For Well 3
Arps
Modified Arps
PLE
Series Model
Methods Arps Modified Arps PLE Series Model
EUR (MMSTB) 0.393 0.316 0.290 0.373

9. Well 1 – Arps &
Modified Arps
0.0
1.0
2.0
3.0
1.E+02
1.E+03
1.E+04
1.E+05
0 100 200 300 400 500
Gp,BSCForNp,MMSTB
qg,MSCF/day
orqo,STB/day
Time, Days
Arps' Hyperbolic Relation
Cartesian Plot - q and Gp or Np vs. time
qo_STB/day_(hyper)
qo_STB/day_all
qo_STB/day_edited
Np_MMSTB_(hyper)
Np_MMSTB_edited
1
10
100
1000
10000
0.1 1 10 100 1000 10000
q vs t
0
50
100
150
200
250
0
1000
2000
3000
0 200 400 600 800 1000 1200 1400 1600
Np(MSTB)
q(STB/D)
Time (days)
Forecast Arps
q vs t
q vs t Forecast
Np vs t
Forecast Np vs t
0
20
40
60
80
100
120
140
160
180
200
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 200 400 600 800 1000 1200 1400 1600
Np(MSTB)
q(STB/D)
time (days)
Forecast Modified Arps
q vs t
Forecast q vs t
Np vs t
Forecast Np Hyperbolic
Forecast Np ExponentialForecast Comparison
Arps’ DCA EUR – 0.211 MMSTB
Modified Arps’ DCA EUR – 0.179 MMSTB
Arps’ Parameters
b=2
Qi=3962 STB
Di=0.889097 days-1

10. Transient-PI
Well 1 – Transient-PI
0.01
0.1
1
10
100
1000
0.01 0.1 1 10 100 1000 10000 100000
TransientProductivityIndex,J
Material Balance Time (te)
J vs te
Re = 1710 ft
Connected Pore Volume
A*h*φ*ct = 231.5 𝑓𝑡3/psi

11. WELL I RTA
0
1000
2000
3000
4000
Liquidrate[STB/D]
0
40000
80000
Liquidvolume[STB]
Model Option Standard Model, Material Balance
Well Vertical
Reservoir Homogeneous
Boundary Circle, No flow
Tmin 0 hr
Tmax 7296 hr
Total Skin 0.1
k.h, total 171 md.ft
k, average 5.69 md
Pi 7871 psia
STOIIP 2.9 MMSTB
STOIP 2.81 MMSTB
Qo(tmax) 0.0934 MMSTB
Skin 0.1
Pi 7871 psia
k.h 171 md.ft
k 5.69 md
Re - No flow 1830 ft
TMatch 45100 [hr]-1
PMatch 0.00374 [psia]-1
Ab. rate (qa) 0 STB/D
Ab. time (ta) 3128.29 hr
Q(ta) 58106.1 STB
0 4000 8000 12000 16000 20000 24000 28000 32000
Time [hr]
3750
5000
6250
7500
Pressure[psia]
EUR is about 0.117 MMSTB
0
2000
4000
Liquidrate[STB/D]
0
50000
1E+5
1.5E+5
Liquidvolume[STB]
0 4000 8000 12000 16000 20000 24000 28000 32000
Time [hr]
2500
5000
7500
Pressure[psia]
EUR is about 0.178 MMSTB

12. PLE
Well 1 – PLE
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+08
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+00 1.E+02 1.E+04
Gp,MSCForNp,STB
qg,MSCF/dayor
qo,STB/day
Time, days
q and Gp or Np vs. Time, days
qo_wo_Dinf_STB/day_(
PLE_qDb)
qo_w_Dinf_STB/day_(P
LE_qDb)
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04
D-parameter
Time, days
D-parameter vs. Time, days
D_wo_Dinf
D_w_Dinf
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04
b-parameter
Time, days
b-parameter vs. Time, days
b_wo_Dinf
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+00 1.E+02 1.E+04
Dandbparameters
qg,MSCF/dayor
qo,STB/day
Time, days
qDb vs. Time, days
• n = 0.053
• Di^= 3.2581 1/days
• Dinf = 2.69E-03
1/days
• qi^ =29,408 STB/day
EUR= 0.147 MMSTB

13. Well 1 - Comparison
 Well I Forecast
Methods Arps Modified
Arps
PLE RTA
EUR (MMSTB) 0.211 0.179 0.147 0.178
0
50
100
150
200
250
0 200 400 600 800 1000 1200 1400
Np(MSTB)
Time (days)
Reserve Estimation For Well 1
PLE
Arps
Modified Arps
RTA

14. Conclusion
 The forecasts done using different analytical tools
combine well to give the EUR.
 Arps’ DCA overestimates the EUR in both the cases due to
b=2.
 Modified Arps and RTA align well and yield similar results
of EUR.
 In-place volume estimation by RTA and Transient PI align
closely.
 PLE gives the lowest estimates in both the cases and can
be used to predict performance in both transient & BDF
regime.

15. THANK YOU

16. BACKUP
0
50
100
150
200
250
0
1000
2000
3000
0 200 400 600 800 1000 1200 1400 1600
q(STB/D)
time (days)
q vs t
q vs t
q vs t Forecast
Np vs t
Forecast Np vs t
0
20
40
60
80
100
120
140
160
180
200
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 500 1000 1500
Np(STB)
q(STB/D)
time (days)
Forecast Modified Arps
q vs t
Forecast q vs t
Np vs t
Forecast Np Hyperbolic
Forecast Np Exponential
0.0
1.0
2.0
3.0
1.E+02
1.E+03
1.E+04
1.E+05
0 100 200 300 400 500
Gp,BSCForNp,MMSTB
qg,MSCF/day
orqo,STB/day
Time, Days
Arps' Hyperbolic Relation
Cartesian Plot - q and Gp or Np vs. time
qo_STB/day_(hyper)
qo_STB/day_all
qo_STB/day_edited
Np_MMSTB_(hyper)
1
10
100
1000
10000
0.1 1 10 100 1000 10000
q vs t