02_4-Conventional Decline Curve Analysis.ppt

02_4-Conventional Decline Curve A

1. Conventional Decline Curve
Analysis

2. Decline Curve Analysis
Instructional Objectives
•Use conventional decline curve
analysis
•Use effective and nominal decline
equations
•Use exponential and harmonic decline

3. Decline Curve Analysis
Instructional Objectives
•Match past performance
•Forecast future performance

4. Why Do We Use Decline Curve
Analysis?
•Match past performance trends with a
model
–Forecast future
–Estimate reserves

5. What Can Change the Trend?
•Field operations, development
strategies
–Increase or decrease in flowing
bottomhole pressure
–Drilling infill wells
–Drilling stepout wells
–Initiating secondary or tertiary
recovery program

6. The Arps Equation
 
b1
i
i
tbD1
q
tq



7. Assumptions for Arps Equation
•Well is produced at constant
bottomhole pressure
•Well is producing from a reservoir with
fixed, no-flow boundaries
•Well has constant permeability and skin
factor
•Applicable only to boundary-dominated
flow data

8. Hyperbolic Exponent b
 
b1
i
i
tbD1
q
tq



9. 3 Sets of Equations
•Hyperbolic general case
where 0 < b < 1
•Exponential decline where b = 0
•Harmonic decline, where b = 1

10. 0
10
20
30
40
50
60
70
80
90
100
0 5 10 15 20
Time, years
Rate, STB/D Cartesian Rate vs time
Exponential
Hyperbolic
Harmonic

11. 10
100
0 5 10 15 20
Time, years
Rate, STB/D Semilog Rate vs Time
Exponential
Hyperbolic
Harmonic

12. 10
100
0.1 1 10 100
Time, years
Rate, STB/D Harmonic
Log-Log Rate vs Time
Exponential
Hyperbolic

13. 0
50
100
150
200
250
300
350
400
450
0 5 10 15 20
Time, years
Cumulative Production, MSTB Cartesian Cumulative Production
vs Time
Exponential
Hyperbolic
Harmonic

14. 0
10
20
30
40
50
60
70
80
90
100
0 50 100 150 200 250 300 350 400 450
Cumulative Production, MSTB
Rate, STB/D Harmonic
Cartesian Rate vs Cumulative
Production
Exponential
Hyperbolic

15. 10
100
0 50 100 150 200 250 300 350 400 450
Cumulative Production, MSTB
Rate, STB/D Semilog Rate vs Cumulative
Production
Exponential
Hyperbolic
Harmonic

16. 10
100
1 10
(1+b Di t)
Rate, STB/D Log-Log Rate vs (1 + b D
it)
Hyperbolic
Harmonic

17. Hyperbolic Decline (0 < b < 1)
 
b1
i
i
tbD1
q
tq

 

 
b1b1
i
i
b
i
p qq
b1D
q
tN





18. Hyperbolic Decline (0 < b < 1)i
b
a
bD
1r
t

 
 
b1
a
b1
i
i
b
i
pa qq
b1D
q
N





19. Nominal Decline Rate as a
Function of TimetbD1
D
q
q
DD
i
i
b
i
i










  
b1
iei bD11D

   1D1
b
1
D
b
eii 


20. Graphical Analysis for
Hyperbolic Decline10
100
1 10
(1+b Di t)
Rate, STB/D

21. Graphical Analysis for
Hyperbolic Decline0
5
10
15
20
25
0 5 10 15 20
Time, years
-q/(dq/dt)

22. Graphical Analysis for
Hyperbolic Decline0
0.05
0.1
0.15
0.2
0.25
0 5 10 15 20
Time, years
1/q^b

23. Exponential Decline (b = 0)
tD
i
i
eqtq

 

i
i
p
D
tqq
tN



24. Exponential Decline (b = 0)i
a
D
rln
t i
ai
pa
D
qq
N



25. iDD  
e
D1lnD  D
e e1D

 Exponential Decline (b = 0)

26. Graphical Analysis for
Exponential Decline10
100
0 5 10 15 20
Time, years
Rate, STB/D

27. Graphical Analysis for
Exponential Decline0
10
20
30
40
50
60
70
80
90
100
0 50 100 150 200 250 300 350
Cumulative Production, MSTB
Rate, STB/D

28. Harmonic Decline (b = 1)
tD1
q
tq
i
i

  






q
q
ln
D
q
tN
i
i
i
p

29. i
a
D
1r
t

 








a
i
i
i
pa
q
q
ln
D
q
N Harmonic Decline (b = 1)

30. tD1
D
q
q
DD
i
i
i
i

 i
i
ei
D1
D
D

 ei
ei
i
D1
D
D

 Harmonic Decline (b = 1)

31. Graphical Analysis for
Harmonic Decline10
100
0 50 100 150 200 250 300 350 400 450
Cumulative Production, MSTB
Rate, STB/D

32. Nominal vs Effective Decline



dt
tdq
tq
1
dt
tqlnd
tD  i
1i
e
q
qq
D



33. •Nominal decline can be directly converted
from one set of time units to another
•Effective decline cannotbe directly converted
from one set of units to another.
–Conversion depends on hyperbolic
exponent b
–Convert effective to nominal decline in the
original units
–Convert nominal decline to the new units
–Convert nominal decline back to effective
decline in the new units
Nominal vs Effective Decline

34. Example 1
Convert a nominal decline of 12 %/yr to
%/mo

35. Example 1 Solutionmo
%1
mo12
yr1
yr
%12
yr
%12
D
i 













36. Example 2
•Convert an effective decline rate D
e=
12%/yr to %/mo, assuming exponential
decline

37. Example 2 Solution1
010653.0
D
e
mo010596.0
e1
e1D







38. Shifting Time Zero for
Forecasting
pitqq
~
 
pitDD
~
 bb
~
 pttt
~


39. Example 3
•Determine the values of q
i, D
i, and bfor
Well X, using the data in your notes and
the current date, 1/1/97, as time zero.

40. Example 3 Solution
•Part 1 -The updated decline curve
parameters are b= 0.5, q
i= 499.79
STB/D, and D
i= 12.245 %/yr.

41. •Part 2 -The cumulative production from
1/1/97 through 12/30/2000 is 586,152 STB
Example 3 Solution

42. Example 3 Solution
•Part 3 -Cumulative production from
1/1/97 through 12/30/2000:STB159,5866704131256572N
p


43. Estimating b From Reservoir
Drive Mechanism
•Each drive mechanism has a
characteristic b value
•If b cannot be estimated from
production data, b may be estimated
from the drive mechanism

44. Estimating b from Reservoir
Drive Mechanism
References

45. Example 4
1.Estimate the decline curve parameters q
i
and D
ifor a) exponential decline, b)
harmonic decline, and c) hyperbolic
decline with b=0.5.
2.Forecast production for 20 years for a)
exponential decline, b) harmonic decline,
and c) hyperbolic decline with b=0.5.
3.Calculate the ultimate recovery N
paand
the time to abandonment t
afor a field-
wide economic limit rate of 9000 STB/mo.

46. Example 4 Solution
•Prepare the appropriate graphs for
analysis with exponential, harmonic,
and hyperbolic decline and estimate q
i
and D
i
•For convenience, we use time in
months, and plot the production
volume for the month as a monthly rate
at the midpoint of the month
•Develop a new rate table with time in
decimal months

47. Exponential Decline SolutionDecline Curve Example - Exponential Decline
1000
10000
100000
0 60 120 180 240
Time, months
Production rate, STB/month
65700
3490

48. Exponential Decline -Forecast  
 
mo/STB31540e65700eqtq
6010223.1tD
i
2
i


 

STB100,793,2
10223.1
3154065700
D
tqq
tN
2
i
i
p 







49. Exponential Decline -
Abandonment3.7
9000
65700
q
q
r
a
i
 
months5.162
10223.1
3.7ln
D
rln
t
2
i
a 


  
STB100,636,4
10223.1
900065700
D
qq
N
2
i
ai
pa 







50. Harmonic Decline Solution
•For harmonic decline, we graph qvs N
pon
a semilog scale
•First, we have to compute the cumulative
production as a function of time
•Simply adding the monthly volumes will
give the cumulative production at the end
of each month
•Production rate is calculated as an
average over the month, and should be
plotted at the middleof each month

51. Harmonic Decline Solution
•To get cumulative production at the
middle of month j+1, use 
1jj21jp1jjp21jp qq5.0Nq5.0NN
 

52. Harmonic Decline Solution

53. Harmonic Decline Solution
1000
10000
100000
0 500000 1000000 1500000 2000000 2500000 3000000
Cumulative production, STB
Production rate, STB/month

54. Harmonic Decline Solution
0 500000 1000000 1500000 2000000 2500000 3000000
Cumulative production, STB
Production rate, STB/month
1000
10000
100000
68800
31300

55. Harmonic Decline -Forecast
•At t = 60 months, qis calculated from
•Cumulative production N
pat 60 months
is  STB500,796,2
33020
68800
ln
10806.1
68800
q
q
ln
D
q
tN
2
i
i
i
p 



















 
 
mo/STB33020
60101.806+1
68800
tD1
q
tq
2-
i
i






56. Harmonic Decline -
Abandonment6444.7
9000
68800
q
q
r
a
i
  
years6.30months4.367
10806.1
16444.7
D
1r
t
2
i
a 





 STB500,738,7
9000
68800
ln
10806.1
68800
q
q
ln
D
q
N
2
a
i
i
i
pa 


















57. The 20-Year Forecast
1000
10000
100000
0 60 120 180 240
Time, months
Production rate, STB/month

58. Hyperbolic Decline Solution
0.003
0.0035
0.004
0.0045
0.005
0.0055
0.006
0.0065
0.007
0 12 24 36 48 60
Time, months
1/sqrt(q)
3.858E-3
5.583E-3

59.  
yr/%9.17
mo10490.1
5.010858.3
10875.2
ab
m
b
mq
D
12
3
5
b
i
i








 Hyperbolic Decline Solution

60. Hyperbolic Decline -Forecast
    
mo/STB32090
60101.4900.5+1
67200
tbD1
q
tq
5.01
2-
b1
i
i




 

 
 
  
 
 
 
 
 
STB900,786,2
3209067200
5.0110490.1
67200
qq
b1D
q
tN
5.015.01
2
5.0
b1b1
i
i
b
i
p











61. Hyperbolic Decline -
Abandonment4667.7
9000
67200
q
q
r
a
i
  
 
years4.19months6.232
10490.15.0
14667.7
bD
1r
t
2
5.0
i
b
a 





 
 
 
  
 
 
 
 
 
STB100,719,5
900067200
5.0110490.1
67200
qq
b1D
q
N
5.015.01
2
5.0
b1
a
b1
i
i
b
i
pa











62. Hyperbolic Decline -20-Year Forecast
Decline Curve Example -Hyperbolic Decline
1000
10000
100000
0 60 120 180 240
Time, months
Production rate, STB/month

63. Comparison of 20-Year Forecasts for
Exponential, Hyperbolic, and
Harmonic Decline
Decline Curve Example -Comparison of Forecasts
1000
10000
100000
0 60 120 180 240
Time, months
Production rate, STB/month
Field Data
Exponential
Hyperbolic
Harmonic