Elastic Solutions of 1-D Subsidence due to ASR Applications

Applications of aquifer storage and recovery (ASR) technology can cause land subsidence due to the net compression of one or more semi-pervious clay beds. ASR technology is employed to withdraw and inject water from or into aquifers for various purposes. In order to estimate the potential risk of aquifer system deformation in response to an injecting-pumping scheme, a set of four analytic solutions for the one-dimensional case of a conceptual sandwich model are found. Each solution corresponds to one of four different boundary conditions. Each boundary condition comprises a linear change of pore-water pressure with time plus one of four periodic functions. The periodic patterns are trapezoidal, rectangular, triangular, or sinusoidal changes of pressure with time. Solutions are analyzed for a unit column of an idealized compressible semi-pervious layer. A complete mathematical description includes an initial condition, two sets of boundary conditions and a governing equation that is expressed directly in terms of the vertical displacement of the skeletal frame. For simplicity, the saturated aquifer system is assumed to behave like poroelastic material (both recoverable and nonrecoverable). The two idealized aquifers (one above the modeled semi-confining bed and the other beneath) can be pumped independently of each other. Results from the analytic solution are applied to estimate and predict the potential risk of land subsidence due to ASR applications and to provide a first-estimate type of guideline for city and regional planning and the exploitation of water resources.