Author： Keyfitz K.B.L.M.
Publisher： Academic Press
ISSN： 0022-247X
Source： Journal of Mathematical Analysis and Applications, Vol.206, Iss.1, 1997-02, pp. : 205-233
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
Abstract
It is well known that multiphase flow in porous media exhibits hysteresis. This is typically modeled by modifying the saturation dependence of the relative permeabilities. In this paper, a model for hysteretic relative permeabilities is built into the polymer flooding model and the analytical solution to the corresponding Riemann problem is constructed. This produces a nonstrictly hyperbolic system of conservation laws with a history-dependent flux function. Because the polymer model without hysteresis possesses Riemann problem solutions that are not monotonic, the introduction of hysteresis necessarily produces structurally different solutions. We show that hysteresis produces more complicated solutions with more fronts and expansions; and removes some nonuniqueness of solutions.
Related content
Access to resources
Recommend
The Hyperbolic Geometric Flow on Riemann Surfaces
By Kong De-Xing
Communications in Partial Differential Equations, Vol. 34, Iss. 6, 2009-06 ,pp. :
Profile of Blow-up Solution to Hyperbolic System with Nonlocal Term
Acta Mathematica Sinica, Vol. 23, Iss. 6, 2007-06 ,pp. :
The Tacnode Riemann–Hilbert Problem
Constructive Approximation, Vol. 39, Iss. 1, 2014-02 ,pp. :