Speed of Propagation for Some Models of Two-Phase Flow in Porous Media [report]

C. E. Kees
2004 unpublished
Flow of two immiscible, incompressible fluids in a porous medium is typically described by a nonlinear advection-diffusion equation for one of the fluid saturations. The diffusion coefficient, which represents the effect of capillary forces on the fluids, is zero when the medium is locally saturated by either fluid since in these limiting cases the effects of capillary forces tend to zero. This degeneracy in the second-order term usually gives rise to the qualitative property that perturbations
more » ... in saturation propagate with finite speed through regions that are fully saturated by either fluid. This qualitative property is physically realistic. In this work we show that, under certain choices of constitutive relations and modeling approximations, the finite speed of propagation property is lost, despite the fact that the diffusion coefficient is degenerate. The loss of finite speed of propagation is due to unbounded derivatives in the closure relations as the medium becomes saturated by wetting phase. We present analytical and numerical solutions, compare solution dynamics that display finite and infinite speed of propagation, and provide a brief account of numerical difficulties related to the degenerate coefficients. 1 Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES 12 19a. NAME OF RESPONSIBLE PERSON a. REPORT unclassified b. ABSTRACT unclassified c. THIS PAGE unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18
doi:10.21236/ada445637 fatcat:znssjenrkngeradq5frqykv7oi