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On Jacob's Approximation in flow through porous media
Author(s) -
Singh Sita Ram,
Sagar Budhi
Publication year - 1980
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/wr016i002p00377
Subject(s) - linearization , porous medium , mathematics , nonlinear system , richards equation , partial differential equation , mathematical analysis , aquifer , compressibility , discretization , calculus (dental) , porosity , mechanics , geotechnical engineering , geology , physics , groundwater , medicine , dentistry , quantum mechanics , water content
The equation of flow of slightly compressible fluids through nondeformable, or consolidating, porous media is a nonlinear parabolic partial differential equation of the second order. Hitherto, the equation has been approximately linearized by neglecting its nonlinear term. This method of linearization, hereafter called Jacob's method, was first introduced by C. E. Jacob (1950) for flow of groundwater in confined aquifers. In this article the method of functional transformation was used to find a transformation which exactly linearized the equation. A problem of constant drawdown well in extensive homogeneous and isotropic consolidating, or nondeformable, porous media was solved. Solution of the approximately linearized differential equation for the aforesaid problem was compared with the exact one, and the error due to the neglect of the nonlinear term was analyzed. It is shown that the error resulting from Jacob's approximate method of linearization for flow of water through confined aquifers is negligible. However, in the case of the transport of other compressible fluids through nondeformable formations the error is not insignificant.