Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Orientation: DaPrat, et al, paper SPE 13054
Discussion:
This homework concerns the analysis of pressure drawdown and buildup test data for a well in western
Venezuela (Well Mach 3X — 2 tests total, see attached paper by DaPrat, et al). The associated plots
(Cartesian, semilog, and log-log data plots) are attached, as well as the appropriate type curves for dual
porosity systems. As noted in the paper, these well tests are NOT contemporary — i.e., do not "tie" the
pressure drawdown and pressure buildup tests to each other, use the production history as specified for
the pressure buildup test. In short — ANALYZE THESE DATA SEPARATELY!
References:
1. DaPrat, G., Mannucci, J., Prado, L., and Millan, E.: "Use of Pressure Transient Testing to Evaluate
Fractured Reservoirs in Western Venezuela," paper SPE 13054 presented at the 1984 SPE Annual
Conference and Technical Exhibition, Houston, TX, 16-19 September, 1984.
Type Curve Analysis Relations:
Naturally Fractured Reservoir: (pwD' vs. tDλ/(1-ω) format, "Onur, et al " type curves)
Formation Permeability:
k = 141.2
qBμ [ pwD or p'wD ]MP
h
[Δp' or Δp' ]MP
Dimensionless Fracture Storativity:
ω is taken from the type curve match
Dimensionless Interporosity Flow Parameter:
1
λ/(1 − ω )
= 0.0002637
k
[t ]MP
φμct rw2 [t D λ/(1 − ω )]MP
Note: The Cartesian and semilog data analysis techniques are used in exactly the same manner for
natural-ly fractured (i.e., dual porosity) reservoirs as for homogeneous reservoir systems. There are
other interpretation techniques for the semilog analysis of pressure data from naturally fractured
reser-voirs (e.g., those techniques discussed in the second edition of the Lee, et al text), but for the
purpose of this homework, you should only use "conventional" semilog (and Cartesian) data analysis methods.
Required:
1. You are to analyze the well test data in the paper by DaPrat, et al. in as complete detail as possible.
The required data, plots, and instructions are attached.
Notes:
a. Various type curves are provided in a 1 inch-by-1 inch format in this handout — these type curves
should be sufficient for your analysis.
b. You are to provide a comprehensive HAND ANALYSIS of these test data — type curves are provided
for hand analysis..
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
"Cinco-Samaniego" Type Curve
"Cinco-Samaniego" Type Curve: pwD and pwD' vs. tDxf — Various CfD Values (NO WELLBORE STORAGE EFFECTS) (1"x1" format)
2
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
"Cinco-Samaniego" Skin Factor Correlation
"Cinco-Samaniego" Skin Factor Correlation: (used to relate the fractured well case to the Pseudoradial flow skin factor)
3
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Bourdet-Gringarten Type Curve (Unfractured Well)
Bourdet-Gringarten Type Curve: pwD and pwD' vs. tD/CD — Various CD Values (Radial Flow Case — Includes Wellbore Storage and Skin Effects) (1"x1" format)
4
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
"Economides" Type Curve (CfD =1, CDf =various)
"Economides" Type Curve: pwD and pwD' vs. tDxf/CDf — CfD =1 (Fractured Well Case — Includes Wellbore Storage Effects) (1"x1" format)
5
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
"Economides" Type Curve (CfD =2, CDf =various)
"Economides" Type Curve: pwD and pwD' vs. tDxf/CDf — CfD =2 (Fractured Well Case — Includes Wellbore Storage Effects) (1"x1" format)
6
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
"Economides" Type Curve (CfD =2, CDf =various)
"Economides" Type Curve: pwD and pwD' vs. tDxf/CDf — CfD =5 (Fractured Well Case — Includes Wellbore Storage Effects) (1"x1" format)
7
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
"Economides" Type Curve (CfD =10, CDf =various)
"Economides" Type Curve: pwD and pwD' vs. tDxf/CDf — CfD =10 (Fractured Well Case — Includes Wellbore Storage Effects) (1"x1" format)
8
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
"Economides" Type Curve (CfD =1x10-3, CDf =various)
"Economides" Type Curve: pwD and pwD' vs. tDxf/CDf — CfD =1x10-3 (Fractured Well Case — Includes Wellbore Storage Effects) (1"x1" format)
9
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Ansah Type Curve — Pressure Buildup in a Bounded (Closed) Reservoir System
Ansah Type Curve: Pressure Buildup in a Bounded (Closed) Reservoir System (1"x1" format)
10
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Stewart Type Curve — Well in an Infinite-Acting Reservoir System with a Single or Multiple Sealing Faults
Stewart Type Curve: Well in an Infinite-Acting Reservoir System with a Single or Multiple Sealing Faults. (1"x1" format)
11
12
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Type Curves for Naturally Fractured Reservoir Systems (1"x1" Format)
(No Wellbore Storage or Skin Effects)
"Stewart and Ascharsobbi" Type Curve: pwD' vs. tDλ/4 — Various λ and ω Values
"Onur, Satman, and Reynolds" Type Curve: pwD' vs. tDλ/4 — Various λ and ω Values
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Angel Type Curve — Type Curves for Naturally Fractured Reservoir Systems — with Wellbore Storage and Skin Effects
Angel Type Curve: Type Curves for Naturally Fractured Reservoir Systems — with Wellbore Storage and Skin Effects (1"x1" format) (αD=λCD=1x10-1, ω=1x10-1).
13
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Angel Type Curve — Type Curves for Naturally Fractured Reservoir Systems — with Wellbore Storage and Skin Effects
Angel Type Curve: Type Curves for Naturally Fractured Reservoir Systems — with Wellbore Storage and Skin Effects (1"x1" format) (αD=λCD=1x10-2, ω=1x10-1).
14
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Angel Type Curve — Type Curves for Naturally Fractured Reservoir Systems — with Wellbore Storage and Skin Effects
Angel Type Curve: Type Curves for Naturally Fractured Reservoir Systems — with Wellbore Storage and Skin Effects (1"x1" format) (αD=λCD=1x10-3, ω=1x10-1).
15
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Angel Type Curve — Type Curves for Naturally Fractured Reservoir Systems — with Wellbore Storage and Skin Effects
Angel Type Curve: Type Curves for Naturally Fractured Reservoir Systems — with Wellbore Storage and Skin Effects (1"x1" format) (αD=λCD=1x10-4, ω=1x10-1).
16
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Angel Type Curve — Type Curves for Naturally Fractured Reservoir Systems — with Wellbore Storage and Skin Effects
Angel Type Curve: Type Curves for Naturally Fractured Reservoir Systems — with Wellbore Storage and Skin Effects (1"x1" format) (αD=λCD=1x10-1, ω=1x10-2).
17
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Angel Type Curve — Type Curves for Naturally Fractured Reservoir Systems — with Wellbore Storage and Skin Effects
Angel Type Curve: Type Curves for Naturally Fractured Reservoir Systems — with Wellbore Storage and Skin Effects (1"x1" format) (αD=λCD=1x10-2, ω=1x10-2).
18
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Angel Type Curve — Type Curves for Naturally Fractured Reservoir Systems — with Wellbore Storage and Skin Effects
Angel Type Curve: Type Curves for Naturally Fractured Reservoir Systems — with Wellbore Storage and Skin Effects (1"x1" format) (αD=λCD=1x10-3, ω=1x10-2).
19
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Angel Type Curve — Type Curves for Naturally Fractured Reservoir Systems — with Wellbore Storage and Skin Effects
Angel Type Curve: Type Curves for Naturally Fractured Reservoir Systems — with Wellbore Storage and Skin Effects (1"x1" format) (αD=λCD=1x10-4, ω=1x10-2).
20
21
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Well Mach-3X (SPE 13054)
Field Case: Well Mach-3X (SPE 13054)
These data were obtained from a field in Western Venezuela and in this case the analysts claim that the
well performance indicates pseudosteady-state interporosity flow character. You are to verify (or
disprove) this conjecture using both the drawdown and buildup test data. As noted earlier, these drawdown
and buildup tests were not performed at the same relative time in the life of the well.
Reservoir properties:
φ=0.048
rw=0.2917 ft
h=65 ft
Oil properties: (initial reservoir pressure unknown)
Bo=1.8235 RB/STB
μo=0.362 cp
ct=24.5x10-6 psia-1
Production parameters:
Drawdown Test Sequence
qo=2700 STB/D (constant)
pwf(t=0) =11,348.0 psia
Buildup Test Sequence
qo=3224 STB/D (constant)
pwf (Δt=0) = 9911.0 psia
tp=56 hr
Required:
Using the attached plots, you are to perform "type curve" analysis on these data and provide estimates
of the following parameters (as appropriate):
a.
c.
e.
f.
g.
The formation permeability, k.
The dimensionless wellbore storage coefficient, CD.
The near-well skin factor (compare to semilog analysis), s.
The dimensionless fracture storativity ratio, ω.*
The dimensionless interporosity flow coefficient, λ.*
* Assuming that naturally fractured reservoir behavior is exhibited.
Note:
You are also to verify/calculate properties using the specialized plots that are provided (pressure
versus shut-in time and pressure versus logarithm of shut-in time, effective shut-in time, and Horner
time—as well as the Muskat-Arps plot (pressure versus pressure derivative) for the analysis of latetime pressure buildup data). Be sure to perform all Cartesian and semilog analyses (which are
relevant) and provide all results and calculations.
22
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Well Mach-3X (SPE 13054) — Pressure Drawdown Test Sequence
Field Case: Well Mach-3X (SPE 13054) — Pressure Drawdown Test Sequence
Well Test Data Functions:
Point
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
t, hr
0.0
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
7.00
8.00
9.00
10.00
12.00
14.00
16.00
18.00
20.00
24.00
28.00
32.00
36.00
40.00
45.00
50.00
55.00
66.00
67.00
69.00
71.00
74.00
77.00
80.00
84.00
88.00
92.00
96.00
100.00
104.00
108.00
112.00
116.00
120.00
pwf, psia
11348.0
10989.0
10630.0
10486.0
10392.8
10318.5
10268.3
10229.5
10195.4
10141.0
10106.9
10083.2
10063.2
10046.8
10034.3
10022.7
10012.6
9995.6
9981.9
9967.8
9956.1
9933.5
9913.1
9896.7
9879.6
9864.8
9834.1
9806.2
9780.8
9747.0
9723.1
9683.4
9642.7
9608.0
9531.0
9522.8
9508.3
9494.2
9473.1
9452.7
9430.5
9406.2
9377.3
9355.0
9333.2
9311.1
9290.4
9269.4
9251.4
9237.1
9223.0
Δp, psi
0.0
359.0
718.0
862.0
955.2
1029.5
1079.7
1118.5
1152.6
1207.0
1241.1
1264.8
1284.8
1301.2
1313.7
1325.3
1335.4
1352.4
1366.2
1380.2
1391.9
1414.5
1434.9
1451.3
1468.4
1483.2
1513.9
1541.8
1567.2
1601.0
1624.8
1664.6
1705.3
1740.0
1817.0
1825.2
1839.7
1853.8
1874.9
1895.3
1917.5
1941.8
1970.7
1993.0
2014.8
2036.9
2057.7
2078.6
2096.6
2110.9
2125.0
Δp'(t), psi
0.00
517.93
430.07
369.69
313.50
292.20
273.46
252.31
237.76
205.01
184.45
168.72
154.04
145.87
133.37
132.08
125.07
122.71
120.08
120.59
122.29
128.75
136.59
145.01
159.30
168.05
200.42
228.75
254.25
283.91
313.24
348.82
372.69
395.84
429.11
431.85
436.74
440.98
448.00
452.87
467.51
473.87
478.59
486.95
489.22
496.17
498.01
500.18
507.91
505.93
504.41
23
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Well Mach-3X (SPE 13054) — Pressure Drawdown Test Sequence
Field Case: Well Mach-3X (SPE 13054) — Pressure Drawdown Test Sequence (Continued)
Well Test Data Functions:
Point
51
52
53
54
55
56
57
58
59
60
61
62
63
t, hr
131.00
132.00
134.00
136.00
138.00
143.00
148.00
153.00
158.00
163.00
168.00
173.00
178.00
pwf, psia
9181.8
9177.8
9169.7
9161.9
9154.3
9135.4
9117.3
9099.2
9082.5
9064.6
9047.5
9031.1
9015.0
Δp, psi
2166.2
2170.2
2178.3
2186.1
2193.7
2212.6
2230.7
2248.8
2265.5
2283.3
2300.5
2316.9
2333.0
Δp'(t), psi
503.92
511.86
511.80
512.00
512.51
513.35
513.76
514.50
514.64
514.17
515.91
516.69
514.26
24
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Well Mach-3X (SPE 13054) — Pressure Drawdown Test Sequence
Field Case: Well Mach-3X (SPE 13054) — Pressure Drawdown Test Sequence
Cartesian Plot: "Wellbore Storage" Plot
Semilog Plot: Pressure versus Time Data
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Well Mach-3X (SPE 13054) — Pressure Drawdown Test Sequence
Field Case: Well Mach-3X (SPE 13054) — Pressure Drawdown Test Sequence
Log-log Plot: Pressure Drop and Pressure Drop Derivative versus Time Data (1 inch x 1 inch)
25
26
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Well Mach-3X (SPE 13054) — Pressure Buildup Test Sequence
Field Case: Well Mach-3X (SPE 13054) — Pressure Buildup Test Sequence
Well Test Data Functions:
Point
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Δt,
hr
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
3.00
3.50
4.00
5.00
6.00
7.00
8.00
9.00
10.00
12.00
14.00
16.00
18.00
20.00
24.00
28.00
32.00
36.00
40.00
45.00
50.00
55.00
70.00
72.00
75.00
79.00
83.00
87.00
92.00
97.00
102.00
107.00
112.00
117.00
122.00
127.00
138.00
140.00
142.00
145.00
Δte,
hr
0.00
0.25
0.50
0.74
0.98
1.22
1.46
1.70
1.93
2.16
2.39
2.85
3.29
3.73
4.59
5.42
6.22
7.00
7.75
8.48
9.88
11.20
12.44
13.62
14.74
16.80
18.67
20.36
21.91
23.33
24.95
26.42
27.75
31.11
31.50
32.06
32.77
33.44
34.07
34.81
35.50
36.15
36.76
37.33
37.87
38.38
38.86
39.84
40.00
40.16
40.40
(tp+Δt)/Δt
∞
2.2500E02
1.1300E02
7.5667E01
5.7000E01
4.5800E01
3.8333E01
3.3000E01
2.9000E01
2.5889E01
2.3400E01
1.9667E01
1.7000E01
1.5000E01
1.2200E01
1.0333E01
9.0000E00
8.0000E00
7.2222E00
6.6000E00
5.6667E00
5.0000E00
4.5000E00
4.1111E00
3.8000E00
3.3333E00
3.0000E00
2.7500E00
2.5556E00
2.4000E00
2.2444E00
2.1200E00
2.0182E00
1.8000E00
1.7778E00
1.7467E00
1.7089E00
1.6747E00
1.6437E00
1.6087E00
1.5773E00
1.5490E00
1.5234E00
1.5000E00
1.4786E00
1.4590E00
1.4409E00
1.4058E00
1.4000E00
1.3944E00
1.3862E00
pws,
psia
9911.0
10095.0
10255.0
10451.0
10564.0
10631.0
10703.0
10743.0
10806.0
10814.0
10830.0
10854.0
10878.0
10878.0
10902.0
10902.0
10917.0
10925.0
10933.0
10941.0
10941.0
10950.0
10959.0
10958.0
10973.0
10982.0
10939.0
10989.0
10989.0
11045.0
11109.0
11109.0
11109.0
11141.0
11149.0
11149.0
11156.0
11165.0
11165.0
11181.0
11181.0
11189.0
11197.0
11200.0
11200.0
11200.0
11200.0
11229.0
11229.0
11252.0
11252.0
Δp,
psi
0.0
184.0
344.0
540.0
653.0
720.0
792.0
832.0
895.0
903.0
919.0
943.0
967.0
967.0
991.0
991.0
1006.0
1014.0
1022.0
1030.0
1030.0
1039.0
1048.0
1047.0
1062.0
1071.0
1028.0
1078.0
1078.0
1134.0
1198.0
1198.0
1198.0
1230.0
1238.0
1238.0
1245.0
1254.0
1254.0
1270.0
1270.0
1278.0
1286.0
1289.0
1289.0
1289.0
1289.0
1318.0
1318.0
1341.0
1341.0
Δp'(Δt),
psi
0.0
220.30
298.85
365.64
378.13
343.81
335.86
291.83
267.04
236.67
205.22
158.34
125.30
102.86
74.52
59.44
50.78
46.09
44.51
41.84
41.41
44.58
51.14
60.74
72.42
93.77
99.76
116.79
130.64
135.97
139.23
146.94
141.97
158.57
168.79
178.69
184.26
185.18
187.37
181.19
180.84
173.67
173.52
166.55
167.23
167.96
169.15
174.65
171.59
175.64
180.98
Δp'(Δte),
psi
0.0
265.20
338.76
354.43
343.78
340.45
302.70
300.09
265.53
243.20
219.14
175.86
141.91
116.87
87.79
73.16
62.15
55.65
53.08
56.31
62.57
83.61
100.20
128.69
141.78
167.70
189.52
237.36
266.22
273.14
285.59
300.55
312.85
332.95
333.23
335.10
337.34
339.55
350.50
352.44
354.12
355.42
356.47
365.64
366.67
367.76
369.45
377.30
382.10
385.93
390.25
27
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Well Mach-3X (SPE 13054) — Pressure Buildup Test Sequence
Field Case: Well Mach-3X (SPE 13054) — Pressure Buildup Test Sequence (Continued)
Well Test Data Functions:
Point
51
52
53
54
55
56
57
58
59
Δt,
hr
148.00
153.00
157.00
160.00
164.00
169.00
174.00
178.00
183.00
Δte,
hr
40.63
41.00
41.28
41.48
41.75
42.06
42.37
42.60
42.88
(tp+Δt)/Δt
1.3784E00
1.3660E00
1.3567E00
1.3500E00
1.3415E00
1.3314E00
1.3218E00
1.3146E00
1.3060E00
pws,
psia
11268.0
11284.0
11292.0
11300.0
11300.0
11308.0
11316.0
11316.0
11316.0
Δp,
psi
1357.0
1373.0
1381.0
1389.0
1389.0
1397.0
1405.0
1405.0
1405.0
Δp'(Δt),
psi
185.83
192.79
195.98
199.63
201.20
204.01
206.54
206.32
206.17
Δp'(Δte),
psi
395.20
412.73
417.38
420.16
423.25
425.78
427.72
429.14
430.96
28
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Well Mach-3X (SPE 13054) — Pressure Buildup Test Sequence
Field Case: Well Mach-3X (SPE 13054) — Pressure Buildup Test Sequence
Cartesian Plot: "Wellbore Storage" Plot
Cartesian Plot: "Muskat" Plot — Pressure versus Pressure Derivative Data
29
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Well Mach-3X (SPE 13054) — Pressure Buildup Test Sequence
Field Case: Well Mach-3X (SPE 13054) — Pressure Buildup Test Sequence
Semilog Plot: "MDH" Plot — Pressure versus Time Data
Semilog Plot: "Horner" Plot — Pressure versus Horner Time Data
Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Well Mach-3X (SPE 13054) — Pressure Buildup Test Sequence
Field Case: Well Mach-3X (SPE 13054) — Pressure Buildup Test Sequence
Log-log Plot: Pressure Drop and Pressure Drop Derivative versus Time Data (1 inch x 1 inch)
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Naturally Fractured Reservoirs (DaPrat, et al, paper SPE 13054)
Well Mach-3X (SPE 13054) — Pressure Buildup Test Sequence
Field Case: Well Mach-3X (SPE 13054) — Pressure Buildup Test Sequence
Log-log Plot: Pressure Drop and Pressure Drop Derivative versus Effective Time Data (1 inch x 1 inch)
31