Deconvolution optimization of pressure and flow rate data from permanent downhole gauges Sanghui Ahn

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Deconvolution optimization of pressure and flow
rate data from permanent downhole gauges
Sanghui Ahn

• Smart Fields Consortium
• March 6, 2008

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Overview

• Deconvolution
• Problem formulation
• Optimization steps
• Results
• Current studies
• Future work

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Convolution and deconvolution
Superposition principle by Duhamel
http//www.fekete.com/resources/media/videos/video
13/index.htm
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Response function
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Superposition
g(t)
q(t)
p(t)
http//www.fekete.com/resources/media/videos/video
13/index.htm
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Real data
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Approach
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Convolution formulation
(log-spaced time)
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1st Optimization step response function

• Objective and constraints for CVX

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Huber penalty function
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Optimization by CVX

• CVX
• Matlab based s/w package for convex programming
• Optimization tool with solver SDPT3/SeDuMi
• Fast in figuring out optimal solution

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2nd Optimization flow rate

• Objective
• Closed form solution
• Choice of the regularization factor

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Target dataset for optimization

• Pressure, flow rate size 2000 points (0.5)
• Knot points for the response function 11
• Iterations 3
• Regularization factor 0.0003 (fixed)

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Response function
1) 1387 2) 300.0 3) 261.1
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Flow rate
1) 458.0 2) 368.7 3) 366.0
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Pressure
1) 27.7 2) 22.94 3) 22.88
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Closer look at pressure and flow rate

• More iterations
• - Pressure matches edges.
  - Flow rate becomes less smooth.

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Trade-off between data residue
Increasing
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Current studies of deconvolution

• By T.von Schroeter et al
• Model formulation
• Optimization

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Future work

• Initial pressure modeling
• Limitation of assuming constant initial pressure
• Representation of the response curvature
• Smoothness
• Adjustment of a regularization factor