Measuring Effective Wellbore Permeability
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Measuring Effective Wellbore Permeability
Sarah Gasda, Princeton University
Michael Celia, Princeton University
Jan Nordbotten, Univ. of Bergen
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Objective
• Propose a simple field test to determine effective (bulk) wellbore permeability
• Use numerical analysis to determine the feasibility of this test– Define the range of detection given
constraints on instrument accuracy
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Approach
• We design a test to determine well permeability.– If we can estimate permeability values for the
formation and caprock, we can find well permeability from pressure response.
• We do this by using simulations to generate response curves that relate pressure response to well permeability.
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Existing Oil and Gas Wells
From IPCC SRCCS, 2005End of 2004End of 2004
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Leakage Pathways in Wells
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Modeling CO2 leakage
• Large spatial and temporal scales
• Multiple leaky wells
– probabilistic framework
• No data exist on wells
– Need to pin down statistical distributions
• Need a simple test to identify kwell in well segments
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Experimental Design
Disturbed zone, kw
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Numerical Experiments
• Standard finite-difference simulator– axi-symmetric coordinates– transient, single-phase flow
• 7 permeable layers (10mD), 7 shale caprocks (0.1mD)– Fixed pressure at top and
outer boundaries– Impermeable bottom
boundary
• Explore parameter space– Vary permeability in well
(kw), caprock (k’), and lower formation (k)
Disturbed zone, kw
r
z
rB
Shale layers
Permeable formations
Fixed pressure B.C.
Lower formation, k
Intermediary caprock, k’
0.5 m
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Example Numerical Results
range ofdetection
Transient data
Steady-state data
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Dimensionless Results
k=10-2 Dk= 1 D
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Limits on Field Measurements
• Instrument measurement accuracy – Pressure transducers rated for high P,T
• ±0.1 bar (Schlumberger, UNIGAGE Quartz)
• Fracture pressure – Minimum horizontal fracture stress ~17 kPa/m
• Bachu et al. 2005. Underground Injection Sci. & Tech.
– Maximum pressure change must be less than fracture pressure minus initial pressure
• Average hydrostatic gradient ~11kPa/m
• Order-of magnitude sensitivity limits• Error in ∆ptop = ±10-2 MPa, ∆pbot ≤ 10 MPa
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Estimation of Sensitivity Limits
• Error in field data – ∆ptop/∆pbot = ±10-3
• Viable range of values – minimum pressure that can
be measured reliably
• Insensitive response regions– Slope of curve is flat
– Small error in ∆ptop translates to large uncertainty in kw
Viable range of values
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Range of Detection
range ofdetection
10 3 d ptop pbot
d kw k
1
1
kw k
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Alternative Test Design
• Purpose– Reduce influence of
lower formation permeability on pressure response
– Expand range of detection
• Move perforations to location within intermediary caprock
• Repeat numerical experiments
intermediary caprock
lower formation
upper formation
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Modified Test Results
k=10-2 Dk= 1 D
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Improved Range of Detection
range ofdetection
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Conclusion
• There is a lack of meaningful data available for well properties.
• A simple downhole pressure test can identify effective well permeability values that are in the critical range of values.
• Field experiments are needed to reduce the uncertainty associated with current estimates of CO2 leakage.
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Thank you!