SPACE TIME MODELING

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Direct SpatiotemporalInterpolation of Reservoir
Flow Responses
Presented by Shekhar Srinivasan
Supervisor Dr. Sanjay Srinivasan
The University of Texas at Austin
Petroleum Geosystems Engineering
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History Matching

• Sensitivity analysis

Porosity
Permeability
Rock fluid compressibilities
Saturations
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History Matching

• Geologist provides prior permeability field
• Change permeability map simulate production
• Check match of production history

Perm field
Change map
Production response
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Objective of Problem
Sampled pressure transients
Desired pressure data
P
P
P
t
t
t
P
15000 ft
?
P
P
t
P
t
t
P
t
t
P
P
t
P
t
t
15000 ft
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Time series modeling

• Fit time series through pressure response
• at sampled wells

Known basis functions
a0
a1
a2

f2 (t)
an



fn (t)
f1 (t)
P

sin (w t )
P
c y t
e -t
t
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Wavelets A Handy Tool
Scale 2
Scale 1
Original image
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Inverse transform
Scale 2
Scale 1
Reconstructed image
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Scaling Translation
Scaling parameter m
Translation parameter n
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Identify structure
Sm(32)

• Isolate noise from signal
• Average - smooth structure
• Details noise (no structure)
• Averages split further

(16)Am-1
Dm-1(16)
Dm-2(8)
(8)Am-2
(4)Am-3
Dm-3(4)

Noise
Trend
Transient map
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Well Model
Plot map at various scales
15000 ft
15000 ft
15000 ft
15000 ft

• Underlying permeability field unknown
• Pressure history measured at wells is decomposed
  using wavelets
• Maps of coefficients are plotted at different
  scales

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Infer spatial variability
3rd time window
1st time window
4th time window
2nd time window

• Observe
• 1st time window shows effect of fluid
  compressibility
• 2nd, 3rd, 4th windows show effect of underlying
  geology flow rate

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Information Networking
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Model spatial correlation

• Small variability for closely spaced locations
  due to identical responses
• Variability increases with lag spacing

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Sequential simulation
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Simulated maps at various scales
3rd time window
1st time window
4th time window
2nd time window

• OBSERVE
• Spatial variability at multiple scales distinctly
  visible
• Reinforce multiscale reservoir operation

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Reconstruction

• Collect coefficients from simulated maps
• Inverse wavelet transform

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Summary
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Pressure data
Wavelet decomp
Coefficients
At all wells
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Semivariogram
Interpolation
Maps
Reconstruction
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Advantages

• Quicker technique for reservoir model validation
• Optimal location of wells based on predicted
  pressure response
• General technique used for hydrogeological
  environmental remediation problems

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Questions?