Data mining
Interpretation of Data from Permanent Downhole Gauges, Using Data Mining Approaches Yang Liu and Roland N. Horne
ConocoPhillips, Stanford University
1 March 26, 2014
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Table of Contents • • • • •
Introduction Kernelized Data Mining Application Performance Analysis Summary and Future Work
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Table of Contents • • • • •
Introduction Kernelized Data Mining Application Performance Analysis Summary and Future Work
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Permanent Downhole Gauges • Long time (up to 10 years), high frequency (1 measurement/10s) • Huge volume (>1 GB/year) • Noisy (< 1% noise)
M. Konopczynski and C. McKay, 2009
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Pressure and Flow Rate Pressure (psi)
9000 8900 8800 8700 8600 260
280
300
320
340
360
380
340
360
380
Time (hours) Flow Rate (STB/d)
4
2.5
x 10
2 1.5 1 0.5 0 260
280
300
320
Time (hours) A typical pressure and flow rate data measured from permanent downhole gauge (PDG)
• Measurements were obtained and stored, but not used as much as they could be. • Hidden in the PDG data, there should be some useful information that would help to better describe the reservoir. March 26, 2014
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Problems • The data are very noisy.
9000
Pressure (psi)
Pressure (psi)
• Commonly only buildup (zero flow rate) data are utilized. 8900 8800 8700 8600 260
280
300
320
340
360
380
8704 8703 8702 8701 8700 319.4 319.6 319.8
2 1
280
300
320
340
360
380
Flow Rate (STB/d)
Flow Rate (STB/d)
x 10
0 260
320.2 320.4 320.6 320.8
321
321.2 321.4
321
321.2 321.4
Time (hours)
Time (hours) 4
3
320
4
1.945
x 10
1.94 1.935 1.93 319.4 319.6 319.8
Time (hours)
320
320.2 320.4 320.6 320.8
Time (hours)
• Flow rate information are not • A predefined physical model is incorporated in the interpretation. required in advance. March 26, 2014
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Not All “Noise” is Noise 9362
9470
pressure 9361.5
9460
9361
9450
9360.5
9440
flow
B
A
9360
9430
9359.5
9420 p q
9359
9410
A – flow event 9358.5
B – noise event
7 9400
Research Target (1) Data
Cleaned Data 5000
Pressure (psi)
Pressure (psi)
5000
4500
4000 0
20
40
60
80
100
120
140
160
180
200
4800 4600 4400 4200 0
20
40
60
Flow Rate (STB/d)
Flow Rate (STB/d)
60 40 20 0 20
40
60
80
100
120
100
120
140
160
180
200
140
160
180
200
Time (hours)
Time (hours)
0
80
140
160
180
200
Time (hours)
60 40 20 0 0
20
40
60
80
100
120
Time (hours)
• How to utilize the whole noisy data set to make interpretation? March 26, 2014
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Research Target (2) Reservoir Model
9000
Pressure (psi)
Pressure (psi)
Data 8900 8800 8700 8600 260
280
300
320
340
360
380
10000
9000
8000
7000 0
20
Flow Rate (STB/d)
Flow Rate (STB/d)
x 10 2 1.5 1 0.5
280
300
320
340
60
80
100
120
100
120
Time (hours)
Time (hours) 4
0 260
40
360
380
Time (hours)
4
x 10 8 7.5 7 6.5 6 0
20
40
60
80
Time (hours)
• Reservoir model should be revealed without knowing it in advance. March 26, 2014
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Data Mining Overview • Spam email classification • Hand written zip code identification • Google Translate • Data mining is the process of extracting patterns (reservoir models) from data (PDG data). March 26, 2014
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Work Flow Pressure (psi)
𝑝(𝑡)
Flow Rate (STB/D)
71
𝑞(𝑡)
70.5
𝑝 = 𝑓(𝑞, 𝑡)
70 69.5 69
0
5
10
15
20
8700 8600 260
280
300
320
340
360
380
340
360
380
4
3
x 10
2 1 0 260
280
300
320
Time (hours)
Predict
Pressure prediction 3600
3500
3400
Pressure (psi)
Feed
8800
Flow Rate (STB/d)
𝑞(𝑡)
Training process
New flow rate history
8900
Time (hours)
PDG Data
Understanding of the reservoir (in data mining algorithm)
9000
𝑝 (𝑡)
3300
3200
3100
25
Time (hours)
3000
2900
0
5
10
15
20
25
Time(hours)
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Table of Contents • • • • •
Introduction Kernelized Data Mining Application Performance Analysis Summary and Future Work
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Key Elements of Data Mining Cost Function Model as pattern structure Underlying functional form sought from data.
𝑦 pred = h𝛉 𝐱 = 𝛉T ϕ 𝐱
Judging the quality of field model to data.
𝐽 𝛉 =
1 2
𝑚
h𝛉 𝐱
𝑖
− 𝑦 (𝑖)
2
𝑖=1
Optimization Method Minimizing cost function on training data set.
Conjugate Gradient Optimization
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Linearity in Feature Space y a0 a1z a2z 2 a3z 3
y θT x
x
1 x z Only capture the linearity • •
y θ x T
1 z x 2 z z 3 Capture the 3rd order nonlinearity
Performance: The more nonlinearity you want to capture, the more complex ϕ(𝐱) will be. How to run data mining in feature space without explicitly writing out ϕ(𝐱) ?
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Kernel Function • • • •
Use kernel function to split the calculation and the learning process. Defined by inner product: K 𝐱, 𝐳 = ϕ 𝐱 T ϕ(𝐳). Calculate kernel function using 𝐱 and 𝐳 only. Calculating in low dimensional space (the space of 𝐱), while learning in high dimensional space (the space of ϕ(𝐱)).
Prove: 𝐓
𝟐
𝟐
𝐊 𝐱, 𝐳 = 𝐱 𝒛 = 𝒙𝟏 𝒛𝟏 + 𝒙𝟐 𝒛𝟐 + 𝒙𝟑 𝒛𝟑 = 𝒙𝟐𝟏 𝒛𝟐𝟏 + 𝒙𝟐𝟐 𝒛𝟐𝟐 + 𝒙𝟐𝟑 𝒛𝟐𝟑 + 𝟐𝒙𝟏 𝒛𝟏 𝒙𝟐 𝒛𝟐 + 𝟐𝒙𝟏 𝒛𝟏 𝒙𝟑 𝒛𝟑 + 𝟐𝒙𝟐 𝒛𝟐 𝒙𝟑 𝒛𝟑 = 𝒙𝟏 𝒙𝟏 , 𝒙𝟏 𝒙𝟐 , 𝒙𝟏 𝒙𝟑 , 𝒙𝟐 𝒙𝟏 , 𝒙𝟐 𝒙𝟐 , 𝒙𝟐 𝒙𝟑 , 𝒙𝟑 𝒙𝟏 , 𝒙𝟑 𝒙𝟐 , 𝒙𝟑 𝒙𝟑 𝒛𝟏 𝒛𝟏 , 𝒛𝟏 𝒛𝟐 , 𝒛𝟏 𝒛𝟑 , 𝒛𝟐 𝒛𝟏 , 𝒛𝟐 𝒛𝟐 , 𝒛𝟐 𝒛 𝟑 , 𝒛𝟑 𝒛𝟏 , 𝒛𝟑 𝒛𝟐 , 𝒛𝟑 𝒛𝟑 𝑻 Considering 𝐊 𝐱, 𝐳 = 𝛟 𝐱 𝐓 𝛟(𝐳), we have 𝛟(𝐱) = 𝒙𝟏 𝒙𝟏 , 𝒙𝟏 𝒙𝟐 , 𝒙𝟏 𝒙𝟑 , 𝒙𝟐 𝒙𝟏 , 𝒙𝟐 𝒙𝟐 , 𝒙𝟐 𝒙𝟑 , 𝒙𝟑 𝒙𝟏 , 𝒙𝟑 𝒙𝟐 , 𝒙𝟑 𝒙𝟑 𝑻 , and 𝛟 𝒛 = 𝒛𝟏 𝒛𝟏 , 𝒛𝟏 𝒛𝟐 , 𝒛𝟏 𝒛𝟑 , 𝒛𝟐 𝒛𝟏 , 𝒛𝟐 𝒛𝟐 , 𝒛𝟐 𝒛𝟑 , 𝒛𝟑 𝒛𝟏 , 𝒛𝟑 𝒛𝟐 , 𝒛𝟑 𝒛𝟑 𝑻 .
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K 𝐱, 𝐳 =
2 T 𝐱 𝐳
𝐱 = 𝒙𝟏 , 𝒙𝟐 , 𝒙𝟑 𝐓 , 𝐳 = 𝒛𝟏 , 𝒛𝟐 , 𝒛𝟑
𝜙 𝐱 =
𝐓
𝒙𝟏 𝒙𝟏 𝒙𝟏 𝒙𝟐 𝒙𝟏 𝒙𝟑 𝒙𝟐 𝒙𝟏 𝒙𝟐 𝒙𝟐 𝒙𝟐 𝒙 𝟑 𝒙𝟑 𝒙𝟏 𝒙𝟑 𝒙𝟐 𝒙𝟑 𝒙𝟑
We are making the calculation in 3dimensional space (the space of vector x), while running the learning algorithm in the 9dimensional space (the space of ϕ(𝐱)).
15
Convolution Kernel • Created in artificial linguistic study • Words comparison: “move” vs. “remove” – 𝑢𝑖 ∈ {𝑝𝑎𝑟𝑡𝑠 𝑜𝑓 "move"}: m, o, v, e, mo, ov, ve, mov, ove, move – 𝑣𝑗 ∈ {𝑝𝑎𝑟𝑡𝑠 𝑜𝑓 "remove"}: r, e, m, o, v, re, em, mo, ov, ve, rem, emo, mov, ove, remo, emov, move, remov, emove, remove – Compare parts using a given kernel: k(𝑢𝑖 , 𝑣𝑗 ) – Sum all kernels of parts to form a new kernel:
• K "move", "remove" =
10 𝑖=1
20 𝑗=1 𝑘(𝑢𝑖 , 𝑣𝑗 )
• PDG data: – Decompose the pressure transient into a series of pressure responses to the previous flow rate change events. – Treat all previous points as breakpoints so that no breakpoint detection is needed. – The superposition was then reflected as the summation of simple kernels evaluated on all parts (hence superposition over kernelization). March 26, 2014
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Convolution Kernel (Method D)
j
i
K x (i ) , x ( j ) k x (ki ) , x l( j )
k 1 l 1
(i ) k
k x ,x Flow Rate (STB/d)
80
x x (i ) T k
( j) l
t 2i
60 40
( j) l
𝒌𝒕𝒉 flow rate change
i
q1
i
q2
x (ki )
x i
20 0
10
i t 1 30 20
40
50
60
70
qki qki log t ki i i qk t k i i qk t k
Time(hours) March 26, 2014
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Time elapsed from 𝒌𝒕𝒉 flow rate change
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Training and Prediction • Training: 𝐊𝛃 = 𝐲, where 𝐊 𝑖,𝑗 = K 𝐱 𝑖 , 𝐱
𝑗
, and 𝛃 = 𝛽1 , 𝛽2 , … , 𝛽𝑚
T
• Prediction: 𝑦 pred =
𝑚 𝑖 𝑖=1 𝛽𝑖 K(𝐱
, 𝐱 pred )
• Essentially, we are using K 𝐱 𝑖 ,∙ as the basis to describe the PDG data space. • Conjugate gradient method to solve 𝐊𝛃 = 𝐲
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Table of Contents • • • • •
Introduction Kernelized Data Mining Application Performance Analysis Summary and Future Work
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Simple Synthetic Case: Training Data Pressure (psi)
0
True Data Noisy Data
-500
-1000 0
20
40
60
80
100
120
140
160
180
200
Flow Rate (STB/d)
Time (hours) 80 60 40
True Data
20
Noisy Data
0 0
20
40
60
80
100
120
140
160
180
200
Time (hours)
Wellbore effect, skin, radial flow, and constant pressure boundary are all present. March 26, 2014
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Simple Synthetic Case: Test Data Pressure (psi)
0
Constant pressure boundary with wellbore effect and skin factor
-500
-1000 0
20
40
60
80
100
120
140
160
180
200
140
160
180
200
Flow Rate (STB/d)
Time (hours) 80 60 40 20 0 0
20
40
60
80
100
120
Time (hours) 0
Pressure (psi)
Pressure (psi)
-600
-700
-800
-900 0
10
20
30
40
50
60
70
80
-200 -400 -600 -800 0
20
40
60
80 75 70 65 60 0
10
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30
40
50
100
120
140
160
180
200
140
160
180
200
Time (hours) Flow Rate (STB/d)
Flow Rate (STB/d)
Time (hours)
80
60
70
80
Time (hours)
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60 40 20 0 0
20
40
60
80
100
120
Time (hours)
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Simple Synthetic Case: Test Results 0
True Data
-100
Method D
Constant pressure boundary with wellbore effect and skin factor
Pressure (psi)
-200
-300
-400
-500
-600
-700
-800
-900 0
20
40
60
80
100
120
140
160
180
200
Time (hours) 3
0
10
True Data -100
Method D Pressure (psi)
Pressure (psi)
-200
2
10
True Data True Data (Derivative) Method D 1
-300
-400
-500
-600
-700
Method D (Derivative)
10 0 10
1
10
-800
2
10
0
Time (hours)
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40
60
80
100
120
140
160
180
200
Time (hours)
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Complicated Synthetic Case
Wellbore effect, skin, radial flow, and constant pressure boundary are all present. True Data
-200
-400
Method D -600 -300
-800
Pressure (psi)
Pressure (psi)
-200
-1000 0
20
40
60
80
100
120
140
Time (hours)
160
180
200
True Data
Flow Rate (STB/d)
Noisy Data 80 60
-400
-500
-600
-700
40 20
-800
0
20
40
60
80
100
120
140
160
180
0
200
Time (hours)
3
20
40
60
80
100
120
140
160
180
200
Time (hours)
0
10
True Data -100
Method D Pressure (psi)
Pressure (psi)
-200
2
10
-300
-400
-500
-600
True Data True Data (Derivative) Method D 1
-700
Method D (Derivative)
10 0 10
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10
Time (hours)
0
2
10
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20
40
60
80
100
120
Time (hours)
140
160
180
200
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Semi-Real Case
Wellbore effect, skin, radial flow, and constant pressure boundary are all present. 0
True Data
True Data -500
Noisy Data
Method D
-200
-1000
Pressure (psi)
Pressure (psi)
0
-1500 0
20
40
60
80
100
120
140
160
180
200
Flow Rate (STB/d)
Time (hours) 80 60
-400
-600
-800
40
True Data
20
-1000
Noisy Data
0 0
20
40
60
80
100
120
140
160
180
200
-1200 0
Time (hours)
20
40
60
80
100
120
140
160
180
200
Time (hours)
3
10
0
True Data -100
Method D Pressure (psi)
Pressure (psi)
-200
2
10
True Data True Data (Derivative) Method D 1
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-400
-500
-600
-700
Method D (Derivative)
10 0 10
-300
1
10
Time (hours)
2
10
-800 0
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20
40
60
80
100
120
Time (hours)
140
160
180
200
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Real Case (I) Real Data
0 -100
Real Data
-100 -200 -300 -400 332
334
336
338
340
342
344
346
348
350
352
Time (days) 4
x 10
Flow Rate (STB/d)
Method D
-150
Pressure (psi)
Pressure (psi)
-50
2 1.5 1
-200
-250
-300
-350
0.5
Real Data
0 332
334
336
338
340
342
344
346
348
350
-400 332
352
334
336
338
Time (days)
340
342
344
346
348
350
352
Time (days)
2
0
10
Method D
-1
-3
1
Pressure (psi)
Pressure (psi)
-2
10
0
10
-4 -5 -6 -7 -8
Method D 10
-9
Method D (Derivative)
-1 0
10
1
10
2
10
-10
3
10
0
Time (days)
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40
60
80
100
120
140
160
180
200
Time (days)
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Real Case (II) 0
-200 -100
-400 -600
Pressure (psi)
Pressure (psi)
100
0
Real Data
-800 500
550
600
650
700
750
800
Time (days) 4
Flow Rate (STB/d)
x 10 2
Real Data
1.5
-200
-300
-400
-500
-600
Real Data
1 -700
0.5
Method D
0 500
550
600
650
700
750
-800 500
800
520
540
Time (days)
560
580
600
620
640
660
680
Time (days)
2
100
10
0
-100
1
Pressure (psi)
Pressure (psi)
10
0
10
-1
10
-200
-300
-400
-500
-600
Real Data
Method D
Method D
Method D (Derivative)
-2
10
-700
0
10
1
10
2
10
-800 500
3
10
Time (days)
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600
650
700
750
800
Time (days)
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Table of Contents • • • • •
Introduction Kernelized Data Mining Application Performance Analysis Summary and Future Work
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Performance Analysis • • • • • •
Outliers Aberrant segments Incomplete production history Unknown initial pressure Sampling frequency Evolution of learning
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Performance Analysis • • • • • •
Outliers Aberrant segments Incomplete production history Unknown initial pressure Sampling frequency Evolution of learning
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Outliers
6% of pressure and 3% of flow rate training data are outliers; 3% artificial normal noise everywhere. 0
True Data
0
True Data
-100
Noisy Data
Method D
-500
-200
-1000
Pressure (psi)
Pressure (psi)
500
-1500 0
20
40
60
80
100
120
140
160
180
200
Flow Rate (STB/d)
Time (hours) 80 60 40
-300
-400
-500
-600
-700
True Data
20 0
Noisy Data
-20 0
20
40
60
-800
80
100
120
140
160
180
200
-900 0
Time (hours)
20
40
60
80
100
120
140
160
180
200
Time (hours)
3
10
0
True Data -100
Method D Pressure (psi)
Pressure (psi)
-200
2
10
True Data True Data (Derivative)
-300
-400
-500
-600
Method D -700
Method D (Derivative) 1
10 0 10
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10
Time (hours)
2
10
-800 0
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20
40
60
80
100
120
Time (hours)
140
160
180
200
30
Aberrant Segments (I)
8% of pressure training data lay in an aberrant segment; 3% artificial normal noise everywhere. 0
True Data
Method D
-500
-200
aberrant segment -1000 0
20
40
60
80
100
120
140
160
180
200
Flow Rate (STB/d)
Time (hours) 80 60 40
Noisy Data
0 0
20
40
60
80
-300
-400
-500
-600
-700
True Data
20
True Data
-100
Noisy Data
Pressure (psi)
Pressure (psi)
0
-800
100
120
140
160
180
200
-900 0
Time (hours)
20
40
60
80
100
120
140
160
180
200
Time (hours)
3
10
0
True Data -100
Method D Pressure (psi)
Pressure (psi)
-200
2
10
True Data True Data (Derivative)
-300
-400
-500
-600
Method D -700
Method D (Derivative) 1
10 0 10
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10
Time (hours)
2
10
-800 0
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40
60
80
100
120
Time (hours)
140
160
180
200
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Aberrant Segments (II) 0
-200
-100
True Data
-400
-200
Method D
aberrant segment
-600
-300
Pressure (psi)
Pressure (psi)
8% of pressure training data lay in an aberrant segment; 3% artificial normal noise everywhere. 0
-800 0
20
40
60
80
100
120
140
Flow Rate (STB/d)
Time (hours)
160
180
200
True Data Noisy Data
60 40
-400 -500 -600 -700 -800
20 0
-900
0
20
40
60
80
100
120
140
160
180
200
-1000 0
Time (hours)
20
40
60
80
100
120
140
160
180
200
Time (hours)
3
10
0
True Data -100
Method D Pressure (psi)
Pressure (psi)
-200
2
10
True Data True Data (Derivative)
-300
-400
-500
-600
Method D -700
Method D (Derivative) 1
10 0 10
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10
Time (hours)
2
10
-800 0
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40
60
80
100
120
Time (hours)
140
160
180
200
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Aberrant Segments (III)
8% of pressure training data lay in an aberrant segment (removed); 3% artificial normal noise everywhere. 0
Pressure (psi)
0
Method D
-400
-200
Pressure (psi)
data removed
-600 -800 0
20
40
60
80
100
120
140
Time (hours) Flow Rate (STB/d)
True Data
-100
-200
160
180
200
True Data Noisy Data
60 40
-300
-400
-500
-600
-700
20 -800
0 0
20
40
60
80
100
120
140
160
180
200
-900 0
Time (hours)
20
40
60
80
100
120
140
160
180
200
Time (hours)
3
10
0
True Data -100
Method D Pressure (psi)
Pressure (psi)
-200
2
10
True Data True Data (Derivative)
-300
-400
-500
-600
Method D -700
Method D (Derivative) 1
10 0 10
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10
Time (hours)
2
10
-800 0
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40
60
80
100
120
Time (hours)
140
160
180
200
33
Flow Rate (STB/d) Pressure (psi)
Incomplete Production History 500 0 -500
True Data Noisy Data
-1000 -1500
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0
50
100
150
200
250
300
250
300
Time (hours) 100
True Data Noisy Data 50
0 0
50
100
150
200
Time (hours)
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Effective Rate Correction 3
-400
10
True Data Method D
Pressure (psi)
Without effective rate correction
Pressure (psi)
-500
-600
-700
-800
-900
2
10
True Data True Data (Derivative) Method D Method D (Derivative)
-1000 1
-1100 100
120
140
160
180
200
220
240
260
280
300
10 0 10
Time (hours)
-500
Pressure (psi)
𝑡 (1) 𝑞1 = 𝑞eff
3
-600
-700
-800
-900
2
10
True Data True Data (Derivative) Method D Method D (Derivative)
-1000
-1100 100
1
120
140
160
180
200
220
240
260
280
Time (hours)
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10
True Data Method D
-400
Pressure (psi)
𝑞eff =
𝑄 (1)
2
10
Time (hours)
-300
With effective rate correction
1
10
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10 0 10
1
2
10
10
Time (hours)
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Table of Contents • • • • • • •
Introduction Kernelized Data Mining Application Performance Analysis Scalability Simple Kernel Methods Summary and Future Work
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Summary •
•
•
•
•
•
The nonparametric data mining algorithms do not require any physical model or mathematical assumption ahead of time. As long as the algorithm puts all the possible features in the input vector, the data mining methods will find a suitable functional form in the high-dimensional space and thereby discover the most appropriate reservoir model in the process. The data mining approaches cointerpret the pressure and flow rate data simultaneously by utilizing both the pressure and the flow rate in the training process. This provides a way to make use of flow rate measurements that can now be recorded with some modern PDG tools. The data mining methods do not require constant flow rate, and utilize the whole set of variable flow rate PDG data. The procedures also work well in the absence of any shut-in periods, which are generally required for present analysis techniques. The data mining methods tolerate noise in the data set naturally. No denoising procedure is required in advance, and in fact the procedure provides a robust way of removing noise without removing reservoir response signal. The data mining method enables the flexibility of extracting reservoir model using other measured data from PDG, e.g. temperature. Among Methods A-D, Method D is preferable due to its good accuracy, stability, and no requirement in the knowledge of breakpoints in advance.
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Future Work • • • • •
Unsynchronized data Other data source, e.g. temperature Multiphase flow Multiple wells Parallel computation
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38
Questions
SPE-147298 (2011)
SPE-166440 (2013) SPE-165346 (2013) Thank you March 26, 2014
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39
ConocoPhillips, Stanford University
1 March 26, 2014
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Table of Contents • • • • •
Introduction Kernelized Data Mining Application Performance Analysis Summary and Future Work
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Table of Contents • • • • •
Introduction Kernelized Data Mining Application Performance Analysis Summary and Future Work
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3
Permanent Downhole Gauges • Long time (up to 10 years), high frequency (1 measurement/10s) • Huge volume (>1 GB/year) • Noisy (< 1% noise)
M. Konopczynski and C. McKay, 2009
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4
Pressure and Flow Rate Pressure (psi)
9000 8900 8800 8700 8600 260
280
300
320
340
360
380
340
360
380
Time (hours) Flow Rate (STB/d)
4
2.5
x 10
2 1.5 1 0.5 0 260
280
300
320
Time (hours) A typical pressure and flow rate data measured from permanent downhole gauge (PDG)
• Measurements were obtained and stored, but not used as much as they could be. • Hidden in the PDG data, there should be some useful information that would help to better describe the reservoir. March 26, 2014
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Problems • The data are very noisy.
9000
Pressure (psi)
Pressure (psi)
• Commonly only buildup (zero flow rate) data are utilized. 8900 8800 8700 8600 260
280
300
320
340
360
380
8704 8703 8702 8701 8700 319.4 319.6 319.8
2 1
280
300
320
340
360
380
Flow Rate (STB/d)
Flow Rate (STB/d)
x 10
0 260
320.2 320.4 320.6 320.8
321
321.2 321.4
321
321.2 321.4
Time (hours)
Time (hours) 4
3
320
4
1.945
x 10
1.94 1.935 1.93 319.4 319.6 319.8
Time (hours)
320
320.2 320.4 320.6 320.8
Time (hours)
• Flow rate information are not • A predefined physical model is incorporated in the interpretation. required in advance. March 26, 2014
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Not All “Noise” is Noise 9362
9470
pressure 9361.5
9460
9361
9450
9360.5
9440
flow
B
A
9360
9430
9359.5
9420 p q
9359
9410
A – flow event 9358.5
B – noise event
7 9400
Research Target (1) Data
Cleaned Data 5000
Pressure (psi)
Pressure (psi)
5000
4500
4000 0
20
40
60
80
100
120
140
160
180
200
4800 4600 4400 4200 0
20
40
60
Flow Rate (STB/d)
Flow Rate (STB/d)
60 40 20 0 20
40
60
80
100
120
100
120
140
160
180
200
140
160
180
200
Time (hours)
Time (hours)
0
80
140
160
180
200
Time (hours)
60 40 20 0 0
20
40
60
80
100
120
Time (hours)
• How to utilize the whole noisy data set to make interpretation? March 26, 2014
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Research Target (2) Reservoir Model
9000
Pressure (psi)
Pressure (psi)
Data 8900 8800 8700 8600 260
280
300
320
340
360
380
10000
9000
8000
7000 0
20
Flow Rate (STB/d)
Flow Rate (STB/d)
x 10 2 1.5 1 0.5
280
300
320
340
60
80
100
120
100
120
Time (hours)
Time (hours) 4
0 260
40
360
380
Time (hours)
4
x 10 8 7.5 7 6.5 6 0
20
40
60
80
Time (hours)
• Reservoir model should be revealed without knowing it in advance. March 26, 2014
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Data Mining Overview • Spam email classification • Hand written zip code identification • Google Translate • Data mining is the process of extracting patterns (reservoir models) from data (PDG data). March 26, 2014
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Work Flow Pressure (psi)
𝑝(𝑡)
Flow Rate (STB/D)
71
𝑞(𝑡)
70.5
𝑝 = 𝑓(𝑞, 𝑡)
70 69.5 69
0
5
10
15
20
8700 8600 260
280
300
320
340
360
380
340
360
380
4
3
x 10
2 1 0 260
280
300
320
Time (hours)
Predict
Pressure prediction 3600
3500
3400
Pressure (psi)
Feed
8800
Flow Rate (STB/d)
𝑞(𝑡)
Training process
New flow rate history
8900
Time (hours)
PDG Data
Understanding of the reservoir (in data mining algorithm)
9000
𝑝 (𝑡)
3300
3200
3100
25
Time (hours)
3000
2900
0
5
10
15
20
25
Time(hours)
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Table of Contents • • • • •
Introduction Kernelized Data Mining Application Performance Analysis Summary and Future Work
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Key Elements of Data Mining Cost Function Model as pattern structure Underlying functional form sought from data.
𝑦 pred = h𝛉 𝐱 = 𝛉T ϕ 𝐱
Judging the quality of field model to data.
𝐽 𝛉 =
1 2
𝑚
h𝛉 𝐱
𝑖
− 𝑦 (𝑖)
2
𝑖=1
Optimization Method Minimizing cost function on training data set.
Conjugate Gradient Optimization
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Linearity in Feature Space y a0 a1z a2z 2 a3z 3
y θT x
x
1 x z Only capture the linearity • •
y θ x T
1 z x 2 z z 3 Capture the 3rd order nonlinearity
Performance: The more nonlinearity you want to capture, the more complex ϕ(𝐱) will be. How to run data mining in feature space without explicitly writing out ϕ(𝐱) ?
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Kernel Function • • • •
Use kernel function to split the calculation and the learning process. Defined by inner product: K 𝐱, 𝐳 = ϕ 𝐱 T ϕ(𝐳). Calculate kernel function using 𝐱 and 𝐳 only. Calculating in low dimensional space (the space of 𝐱), while learning in high dimensional space (the space of ϕ(𝐱)).
Prove: 𝐓
𝟐
𝟐
𝐊 𝐱, 𝐳 = 𝐱 𝒛 = 𝒙𝟏 𝒛𝟏 + 𝒙𝟐 𝒛𝟐 + 𝒙𝟑 𝒛𝟑 = 𝒙𝟐𝟏 𝒛𝟐𝟏 + 𝒙𝟐𝟐 𝒛𝟐𝟐 + 𝒙𝟐𝟑 𝒛𝟐𝟑 + 𝟐𝒙𝟏 𝒛𝟏 𝒙𝟐 𝒛𝟐 + 𝟐𝒙𝟏 𝒛𝟏 𝒙𝟑 𝒛𝟑 + 𝟐𝒙𝟐 𝒛𝟐 𝒙𝟑 𝒛𝟑 = 𝒙𝟏 𝒙𝟏 , 𝒙𝟏 𝒙𝟐 , 𝒙𝟏 𝒙𝟑 , 𝒙𝟐 𝒙𝟏 , 𝒙𝟐 𝒙𝟐 , 𝒙𝟐 𝒙𝟑 , 𝒙𝟑 𝒙𝟏 , 𝒙𝟑 𝒙𝟐 , 𝒙𝟑 𝒙𝟑 𝒛𝟏 𝒛𝟏 , 𝒛𝟏 𝒛𝟐 , 𝒛𝟏 𝒛𝟑 , 𝒛𝟐 𝒛𝟏 , 𝒛𝟐 𝒛𝟐 , 𝒛𝟐 𝒛 𝟑 , 𝒛𝟑 𝒛𝟏 , 𝒛𝟑 𝒛𝟐 , 𝒛𝟑 𝒛𝟑 𝑻 Considering 𝐊 𝐱, 𝐳 = 𝛟 𝐱 𝐓 𝛟(𝐳), we have 𝛟(𝐱) = 𝒙𝟏 𝒙𝟏 , 𝒙𝟏 𝒙𝟐 , 𝒙𝟏 𝒙𝟑 , 𝒙𝟐 𝒙𝟏 , 𝒙𝟐 𝒙𝟐 , 𝒙𝟐 𝒙𝟑 , 𝒙𝟑 𝒙𝟏 , 𝒙𝟑 𝒙𝟐 , 𝒙𝟑 𝒙𝟑 𝑻 , and 𝛟 𝒛 = 𝒛𝟏 𝒛𝟏 , 𝒛𝟏 𝒛𝟐 , 𝒛𝟏 𝒛𝟑 , 𝒛𝟐 𝒛𝟏 , 𝒛𝟐 𝒛𝟐 , 𝒛𝟐 𝒛𝟑 , 𝒛𝟑 𝒛𝟏 , 𝒛𝟑 𝒛𝟐 , 𝒛𝟑 𝒛𝟑 𝑻 .
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K 𝐱, 𝐳 =
2 T 𝐱 𝐳
𝐱 = 𝒙𝟏 , 𝒙𝟐 , 𝒙𝟑 𝐓 , 𝐳 = 𝒛𝟏 , 𝒛𝟐 , 𝒛𝟑
𝜙 𝐱 =
𝐓
𝒙𝟏 𝒙𝟏 𝒙𝟏 𝒙𝟐 𝒙𝟏 𝒙𝟑 𝒙𝟐 𝒙𝟏 𝒙𝟐 𝒙𝟐 𝒙𝟐 𝒙 𝟑 𝒙𝟑 𝒙𝟏 𝒙𝟑 𝒙𝟐 𝒙𝟑 𝒙𝟑
We are making the calculation in 3dimensional space (the space of vector x), while running the learning algorithm in the 9dimensional space (the space of ϕ(𝐱)).
15
Convolution Kernel • Created in artificial linguistic study • Words comparison: “move” vs. “remove” – 𝑢𝑖 ∈ {𝑝𝑎𝑟𝑡𝑠 𝑜𝑓 "move"}: m, o, v, e, mo, ov, ve, mov, ove, move – 𝑣𝑗 ∈ {𝑝𝑎𝑟𝑡𝑠 𝑜𝑓 "remove"}: r, e, m, o, v, re, em, mo, ov, ve, rem, emo, mov, ove, remo, emov, move, remov, emove, remove – Compare parts using a given kernel: k(𝑢𝑖 , 𝑣𝑗 ) – Sum all kernels of parts to form a new kernel:
• K "move", "remove" =
10 𝑖=1
20 𝑗=1 𝑘(𝑢𝑖 , 𝑣𝑗 )
• PDG data: – Decompose the pressure transient into a series of pressure responses to the previous flow rate change events. – Treat all previous points as breakpoints so that no breakpoint detection is needed. – The superposition was then reflected as the summation of simple kernels evaluated on all parts (hence superposition over kernelization). March 26, 2014
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Convolution Kernel (Method D)
j
i
K x (i ) , x ( j ) k x (ki ) , x l( j )
k 1 l 1
(i ) k
k x ,x Flow Rate (STB/d)
80
x x (i ) T k
( j) l
t 2i
60 40
( j) l
𝒌𝒕𝒉 flow rate change
i
q1
i
q2
x (ki )
x i
20 0
10
i t 1 30 20
40
50
60
70
qki qki log t ki i i qk t k i i qk t k
Time(hours) March 26, 2014
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Time elapsed from 𝒌𝒕𝒉 flow rate change
17
Training and Prediction • Training: 𝐊𝛃 = 𝐲, where 𝐊 𝑖,𝑗 = K 𝐱 𝑖 , 𝐱
𝑗
, and 𝛃 = 𝛽1 , 𝛽2 , … , 𝛽𝑚
T
• Prediction: 𝑦 pred =
𝑚 𝑖 𝑖=1 𝛽𝑖 K(𝐱
, 𝐱 pred )
• Essentially, we are using K 𝐱 𝑖 ,∙ as the basis to describe the PDG data space. • Conjugate gradient method to solve 𝐊𝛃 = 𝐲
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Table of Contents • • • • •
Introduction Kernelized Data Mining Application Performance Analysis Summary and Future Work
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Simple Synthetic Case: Training Data Pressure (psi)
0
True Data Noisy Data
-500
-1000 0
20
40
60
80
100
120
140
160
180
200
Flow Rate (STB/d)
Time (hours) 80 60 40
True Data
20
Noisy Data
0 0
20
40
60
80
100
120
140
160
180
200
Time (hours)
Wellbore effect, skin, radial flow, and constant pressure boundary are all present. March 26, 2014
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Simple Synthetic Case: Test Data Pressure (psi)
0
Constant pressure boundary with wellbore effect and skin factor
-500
-1000 0
20
40
60
80
100
120
140
160
180
200
140
160
180
200
Flow Rate (STB/d)
Time (hours) 80 60 40 20 0 0
20
40
60
80
100
120
Time (hours) 0
Pressure (psi)
Pressure (psi)
-600
-700
-800
-900 0
10
20
30
40
50
60
70
80
-200 -400 -600 -800 0
20
40
60
80 75 70 65 60 0
10
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20
30
40
50
100
120
140
160
180
200
140
160
180
200
Time (hours) Flow Rate (STB/d)
Flow Rate (STB/d)
Time (hours)
80
60
70
80
Time (hours)
SUPRI-D
60 40 20 0 0
20
40
60
80
100
120
Time (hours)
21
Simple Synthetic Case: Test Results 0
True Data
-100
Method D
Constant pressure boundary with wellbore effect and skin factor
Pressure (psi)
-200
-300
-400
-500
-600
-700
-800
-900 0
20
40
60
80
100
120
140
160
180
200
Time (hours) 3
0
10
True Data -100
Method D Pressure (psi)
Pressure (psi)
-200
2
10
True Data True Data (Derivative) Method D 1
-300
-400
-500
-600
-700
Method D (Derivative)
10 0 10
1
10
-800
2
10
0
Time (hours)
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20
40
60
80
100
120
140
160
180
200
Time (hours)
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Complicated Synthetic Case
Wellbore effect, skin, radial flow, and constant pressure boundary are all present. True Data
-200
-400
Method D -600 -300
-800
Pressure (psi)
Pressure (psi)
-200
-1000 0
20
40
60
80
100
120
140
Time (hours)
160
180
200
True Data
Flow Rate (STB/d)
Noisy Data 80 60
-400
-500
-600
-700
40 20
-800
0
20
40
60
80
100
120
140
160
180
0
200
Time (hours)
3
20
40
60
80
100
120
140
160
180
200
Time (hours)
0
10
True Data -100
Method D Pressure (psi)
Pressure (psi)
-200
2
10
-300
-400
-500
-600
True Data True Data (Derivative) Method D 1
-700
Method D (Derivative)
10 0 10
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-800 1
10
Time (hours)
0
2
10
SUPRI-D
20
40
60
80
100
120
Time (hours)
140
160
180
200
23
Semi-Real Case
Wellbore effect, skin, radial flow, and constant pressure boundary are all present. 0
True Data
True Data -500
Noisy Data
Method D
-200
-1000
Pressure (psi)
Pressure (psi)
0
-1500 0
20
40
60
80
100
120
140
160
180
200
Flow Rate (STB/d)
Time (hours) 80 60
-400
-600
-800
40
True Data
20
-1000
Noisy Data
0 0
20
40
60
80
100
120
140
160
180
200
-1200 0
Time (hours)
20
40
60
80
100
120
140
160
180
200
Time (hours)
3
10
0
True Data -100
Method D Pressure (psi)
Pressure (psi)
-200
2
10
True Data True Data (Derivative) Method D 1
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-400
-500
-600
-700
Method D (Derivative)
10 0 10
-300
1
10
Time (hours)
2
10
-800 0
SUPRI-D
20
40
60
80
100
120
Time (hours)
140
160
180
200
24
Real Case (I) Real Data
0 -100
Real Data
-100 -200 -300 -400 332
334
336
338
340
342
344
346
348
350
352
Time (days) 4
x 10
Flow Rate (STB/d)
Method D
-150
Pressure (psi)
Pressure (psi)
-50
2 1.5 1
-200
-250
-300
-350
0.5
Real Data
0 332
334
336
338
340
342
344
346
348
350
-400 332
352
334
336
338
Time (days)
340
342
344
346
348
350
352
Time (days)
2
0
10
Method D
-1
-3
1
Pressure (psi)
Pressure (psi)
-2
10
0
10
-4 -5 -6 -7 -8
Method D 10
-9
Method D (Derivative)
-1 0
10
1
10
2
10
-10
3
10
0
Time (days)
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20
40
60
80
100
120
140
160
180
200
Time (days)
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Real Case (II) 0
-200 -100
-400 -600
Pressure (psi)
Pressure (psi)
100
0
Real Data
-800 500
550
600
650
700
750
800
Time (days) 4
Flow Rate (STB/d)
x 10 2
Real Data
1.5
-200
-300
-400
-500
-600
Real Data
1 -700
0.5
Method D
0 500
550
600
650
700
750
-800 500
800
520
540
Time (days)
560
580
600
620
640
660
680
Time (days)
2
100
10
0
-100
1
Pressure (psi)
Pressure (psi)
10
0
10
-1
10
-200
-300
-400
-500
-600
Real Data
Method D
Method D
Method D (Derivative)
-2
10
-700
0
10
1
10
2
10
-800 500
3
10
Time (days)
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550
600
650
700
750
800
Time (days)
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Table of Contents • • • • •
Introduction Kernelized Data Mining Application Performance Analysis Summary and Future Work
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Performance Analysis • • • • • •
Outliers Aberrant segments Incomplete production history Unknown initial pressure Sampling frequency Evolution of learning
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Performance Analysis • • • • • •
Outliers Aberrant segments Incomplete production history Unknown initial pressure Sampling frequency Evolution of learning
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Outliers
6% of pressure and 3% of flow rate training data are outliers; 3% artificial normal noise everywhere. 0
True Data
0
True Data
-100
Noisy Data
Method D
-500
-200
-1000
Pressure (psi)
Pressure (psi)
500
-1500 0
20
40
60
80
100
120
140
160
180
200
Flow Rate (STB/d)
Time (hours) 80 60 40
-300
-400
-500
-600
-700
True Data
20 0
Noisy Data
-20 0
20
40
60
-800
80
100
120
140
160
180
200
-900 0
Time (hours)
20
40
60
80
100
120
140
160
180
200
Time (hours)
3
10
0
True Data -100
Method D Pressure (psi)
Pressure (psi)
-200
2
10
True Data True Data (Derivative)
-300
-400
-500
-600
Method D -700
Method D (Derivative) 1
10 0 10
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1
10
Time (hours)
2
10
-800 0
SUPRI-D
20
40
60
80
100
120
Time (hours)
140
160
180
200
30
Aberrant Segments (I)
8% of pressure training data lay in an aberrant segment; 3% artificial normal noise everywhere. 0
True Data
Method D
-500
-200
aberrant segment -1000 0
20
40
60
80
100
120
140
160
180
200
Flow Rate (STB/d)
Time (hours) 80 60 40
Noisy Data
0 0
20
40
60
80
-300
-400
-500
-600
-700
True Data
20
True Data
-100
Noisy Data
Pressure (psi)
Pressure (psi)
0
-800
100
120
140
160
180
200
-900 0
Time (hours)
20
40
60
80
100
120
140
160
180
200
Time (hours)
3
10
0
True Data -100
Method D Pressure (psi)
Pressure (psi)
-200
2
10
True Data True Data (Derivative)
-300
-400
-500
-600
Method D -700
Method D (Derivative) 1
10 0 10
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1
10
Time (hours)
2
10
-800 0
SUPRI-D
20
40
60
80
100
120
Time (hours)
140
160
180
200
31
Aberrant Segments (II) 0
-200
-100
True Data
-400
-200
Method D
aberrant segment
-600
-300
Pressure (psi)
Pressure (psi)
8% of pressure training data lay in an aberrant segment; 3% artificial normal noise everywhere. 0
-800 0
20
40
60
80
100
120
140
Flow Rate (STB/d)
Time (hours)
160
180
200
True Data Noisy Data
60 40
-400 -500 -600 -700 -800
20 0
-900
0
20
40
60
80
100
120
140
160
180
200
-1000 0
Time (hours)
20
40
60
80
100
120
140
160
180
200
Time (hours)
3
10
0
True Data -100
Method D Pressure (psi)
Pressure (psi)
-200
2
10
True Data True Data (Derivative)
-300
-400
-500
-600
Method D -700
Method D (Derivative) 1
10 0 10
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1
10
Time (hours)
2
10
-800 0
SUPRI-D
20
40
60
80
100
120
Time (hours)
140
160
180
200
32
Aberrant Segments (III)
8% of pressure training data lay in an aberrant segment (removed); 3% artificial normal noise everywhere. 0
Pressure (psi)
0
Method D
-400
-200
Pressure (psi)
data removed
-600 -800 0
20
40
60
80
100
120
140
Time (hours) Flow Rate (STB/d)
True Data
-100
-200
160
180
200
True Data Noisy Data
60 40
-300
-400
-500
-600
-700
20 -800
0 0
20
40
60
80
100
120
140
160
180
200
-900 0
Time (hours)
20
40
60
80
100
120
140
160
180
200
Time (hours)
3
10
0
True Data -100
Method D Pressure (psi)
Pressure (psi)
-200
2
10
True Data True Data (Derivative)
-300
-400
-500
-600
Method D -700
Method D (Derivative) 1
10 0 10
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1
10
Time (hours)
2
10
-800 0
SUPRI-D
20
40
60
80
100
120
Time (hours)
140
160
180
200
33
Flow Rate (STB/d) Pressure (psi)
Incomplete Production History 500 0 -500
True Data Noisy Data
-1000 -1500
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0
50
100
150
200
250
300
250
300
Time (hours) 100
True Data Noisy Data 50
0 0
50
100
150
200
Time (hours)
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Effective Rate Correction 3
-400
10
True Data Method D
Pressure (psi)
Without effective rate correction
Pressure (psi)
-500
-600
-700
-800
-900
2
10
True Data True Data (Derivative) Method D Method D (Derivative)
-1000 1
-1100 100
120
140
160
180
200
220
240
260
280
300
10 0 10
Time (hours)
-500
Pressure (psi)
𝑡 (1) 𝑞1 = 𝑞eff
3
-600
-700
-800
-900
2
10
True Data True Data (Derivative) Method D Method D (Derivative)
-1000
-1100 100
1
120
140
160
180
200
220
240
260
280
Time (hours)
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10
True Data Method D
-400
Pressure (psi)
𝑞eff =
𝑄 (1)
2
10
Time (hours)
-300
With effective rate correction
1
10
SUPRI-D
300
10 0 10
1
2
10
10
Time (hours)
35
Table of Contents • • • • • • •
Introduction Kernelized Data Mining Application Performance Analysis Scalability Simple Kernel Methods Summary and Future Work
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Summary •
•
•
•
•
•
The nonparametric data mining algorithms do not require any physical model or mathematical assumption ahead of time. As long as the algorithm puts all the possible features in the input vector, the data mining methods will find a suitable functional form in the high-dimensional space and thereby discover the most appropriate reservoir model in the process. The data mining approaches cointerpret the pressure and flow rate data simultaneously by utilizing both the pressure and the flow rate in the training process. This provides a way to make use of flow rate measurements that can now be recorded with some modern PDG tools. The data mining methods do not require constant flow rate, and utilize the whole set of variable flow rate PDG data. The procedures also work well in the absence of any shut-in periods, which are generally required for present analysis techniques. The data mining methods tolerate noise in the data set naturally. No denoising procedure is required in advance, and in fact the procedure provides a robust way of removing noise without removing reservoir response signal. The data mining method enables the flexibility of extracting reservoir model using other measured data from PDG, e.g. temperature. Among Methods A-D, Method D is preferable due to its good accuracy, stability, and no requirement in the knowledge of breakpoints in advance.
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Future Work • • • • •
Unsynchronized data Other data source, e.g. temperature Multiphase flow Multiple wells Parallel computation
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Questions
SPE-147298 (2011)
SPE-166440 (2013) SPE-165346 (2013) Thank you March 26, 2014
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