Leakage characterization through above-zone pressure monitoring: 1—Inversion approach

Abstract Deep saline aquifers can provide the capacity for disposal/storage of undesirable surface fluids. To maintain containment and thereby prevent leakage of the injected fluids, the target aquifer should be overlain by a confining layer (cap-rock). However, there may be pathways in the cap-rock (e.g., transmissive faults, abandoned wells, active wells that partially penetrate the seal, and local seal weaknesses and fractures) that permit leakage of the injected fluids. Leakage to the subsurface formations may adversely affect the existing and potential energy and mineral resources and shallow ground water resources and soils. As such, detection and characterization of leakage pathways from storage formations into overlying formations are required. In this work, we suggest a flow and pressure test and present an inverse methodology to detect and characterize radially shaped leakage pathways based on the pressure data. The flow test is based on the injection (or production) of water into (or from) a target aquifer at a constant rate. The pressure is measured at a monitoring well in an aquifer overlying the target aquifer, which is separated by a cap-rock. Characterizing the leak based on pressure data involves solution of the leakage inverse problem. We investigate the uniqueness of the solution to the inverse problem through the use of the Hessian matrix and an analytical approach. The stability of the solution is analyzed based on sensitivity coefficients and the correlation matrix. The analyses are applied to a base case problem for which the leak characteristics are obtained over a confidence interval.

[1]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[2]  Kozo Sato,et al.  Monitoring the underground migration of sequestered carbon dioxide using Earth tides , 2006 .

[3]  Fikri J. Kuchuk,et al.  Radius of Investigation for Reserve Estimation From Pressure Transient Well Tests , 2009 .

[4]  Robert W. Zimmerman,et al.  Approximate Solutions for Pressure Buildup During CO2 Injection in Brine Aquifers , 2009 .

[5]  David W. Keith,et al.  Analytical models for determining pressure change in an overlying aquifer due to leakage , 2011 .

[6]  R. Chesnaux,et al.  Detecting and Quantifying Leakage Through Defective Borehole Seals: A New Methodology and Laboratory Verification , 2007 .

[7]  Florian Hollaender,et al.  Pressure transient formation and well testing : convolution, deconvolution and nonlinear estimation , 2010 .

[8]  William H. Press,et al.  Numerical Recipes in FORTRAN - The Art of Scientific Computing, 2nd Edition , 1987 .

[9]  Cem B. Avci,et al.  EVALUATION OF FLOW LEAKAGE THROUGH ABANDONED WELLS AND BOREHOLES , 1994 .

[10]  Clifford H. Thurber,et al.  Parameter estimation and inverse problems , 2005 .

[11]  C. W. Groetsch,et al.  Inverse Problems in the Mathematical Sciences , 1993 .

[12]  C. V. Theis The relation between the lowering of the Piezometric surface and the rate and duration of discharge of a well using ground‐water storage , 1935 .

[13]  Jens Birkholzer,et al.  Analytical solutions for pressure perturbation and fluid leakage through aquitards and wells in multilayered‐aquifer systems , 2011 .

[14]  Ning Liu,et al.  Inverse Theory for Petroleum Reservoir Characterization and History Matching , 2008 .

[15]  Helcio R. B. Orlande,et al.  Inverse and Optimization Problems in Heat Transfer , 2006 .

[16]  Ali H. Dogru,et al.  Confidence Limits on the Parameters and Predictions of Slightly Compressible, Single-Phase Reservoirs , 1977 .

[17]  J. Molson,et al.  A New Method to Characterize Hydraulic Short‐Circuits in Defective Borehole Seals , 2006, Ground water.

[18]  C. McElwee Sensitivity Analysis of Ground-Water Models , 1987 .

[19]  Rajagopal Raghavan,et al.  Well Test Analysis , 2018, Petroleum Engineering.

[20]  M. N. Özişik,et al.  Inverse Heat Transfer: Fundamentals and Applications , 2000 .

[21]  Estimation and Removal of Tidal Effects From Pressure Data , 2009 .

[22]  W. A. Burns,et al.  New Single-Well Test for Determining Vertical Permeability , 1969 .

[23]  George J. Hirasaki Pulse Tests and Other Early Transient Pressure Analyses for In-Situ Estimation of Vertical Permeability , 1974 .

[24]  Vitaly Krasnov,et al.  Interactive Visualization of Uncertainty in Well Test Interpretation , 2004 .

[25]  M. Celia,et al.  Analytical solutions for leakage rates through abandoned wells , 2004 .

[26]  S. Ben Nasrallah,et al.  An inverse problem based on genetic algorithm to estimate thermophysical properties of fouling , 2010 .

[27]  Mehdi Zeidouni,et al.  Leakage characterization through above-zone pressure monitoring: 2—Design considerations with application to CO2 storage in saline aquifers , 2012 .

[28]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.