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Secondary Water Recovery by Air Injection: 1. The Concept and the Mathematical and Numerical Model
Author(s) -
Moridis George J.,
Reddell Donald L.
Publication year - 1991
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/91wr01128
Subject(s) - aquifer , saturation (graph theory) , mechanics , vadose zone , water injection (oil production) , secondary air injection , stage (stratigraphy) , hysteresis , boundary value problem , capillary action , cartesian coordinate system , petroleum engineering , environmental science , geotechnical engineering , mathematics , thermodynamics , engineering , groundwater , geology , physics , geometry , mathematical analysis , paleontology , combinatorics , quantum mechanics
An air‐driven secondary water recovery operation was proposed in order to recover water stored in the unsaturated zone of depleted aquifers and currently unavailable with conventional techniques. The operation employed a single‐well serving as both a production and injection facility and consisted of three stages: (1) an air injection stage, (2) a “recovery” stage, and (3) a “production” (pumping) stage. The concept of the operation was based on the hysteretic behavior of the capillary pressures and the relative permeabilities of air and water. Hysteresis was counted upon to prevent water, forced into the saturated zone during injection, from migrating back to the unsaturated zone. A general mathematical model was developed and numerically approximated using a simultaneous two‐phase, three‐dimensional finite difference model in both Cartesian and cylindrical coordinates. Two types of nonlinearities were identified: (1) pressure‐related weak nonlinearities and (2) saturation‐related strong nonlinearities. Techniques to alleviate the resulting instabilities, as well as methods for the establishment of stable initial conditions and the treatment of boundary conditions, were developed.