caa a22 4500 463163044 CHVBK 20180406164753.0 cr unu---uuuuu 170326e20070201xx s 000 0 eng 10.1007/s11242-006-0019-7 doi (NATIONALLICENCE)springer-10.1007/s11242-006-0019-7 An Approximate Analytical Solution for Counter-Current Spontaneous Imbibition [Elektronische Daten] [Douglas Ruth, Yu Li, Geoffrey Mason, Norman Morrow] An approximate analytical solution is provided for one-dimensional, counter- current, spontaneous imbibition of a wetting phase (water) into a semi-infinite porous medium. The solution is based on the assumption that a similarity solution exists for the displacement process. This assumption, in turn, rests on the assumption that the set of relative permeability and capillary pressures curves are unique functions of saturation and do not depend on the nature of the displacement. It further rests on the assumption that the saturation at the imbibition face does not vary with time. It is demonstrated that the solution is in agreement with results obtained from experiments and also numerical analyses of these experiments. The experiments utilize cylindrical samples with the radial surface and one end-face sealed, and with counter-current imbibition occurring at the open end-face. The stage of the experiment that is modeled by the present solution is the period before the imbibition front contacts the sealed end-face. An important finding of the present analysis is that the pressure upstream of the advancing invasion front is a constant. A second, improved solution is also presented; this solution is an iterative, series solution of an integral-differential equation. It converges to a stable solution in very few terms. Springer, 2007 spontaneous imbibition nationallicence counter-current nationallicence analytical solution nationallicence similarity solution nationallicence integral solution nationallicence series solution nationallicence porous media nationallicence numerical solution nationallicence Ruth Douglas University of Manitoba, R3T 2N2, Winnipeg, Manitoba, Canada aut Li Yu University of Manitoba, R3T 2N2, Winnipeg, Manitoba, Canada aut Mason Geoffrey Loughborough University, Loughborough, UK aut Morrow Norman University of Wyoming, Wyoming, USA aut Transport in Porous Media Kluwer Academic Publishers 66/3(2007-02-01), 373-390 0169-3913 66:3<373 2007 66 11242 https://doi.org/10.1007/s11242-006-0019-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-006-0019-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ruth Douglas University of Manitoba, R3T 2N2, Winnipeg, Manitoba, Canada aut NATIONALLICENCE 700 1- Li Yu University of Manitoba, R3T 2N2, Winnipeg, Manitoba, Canada aut NATIONALLICENCE 700 1- Mason Geoffrey Loughborough University, Loughborough, UK aut NATIONALLICENCE 700 1- Morrow Norman University of Wyoming, Wyoming, USA aut NATIONALLICENCE 773 0- Transport in Porous Media Kluwer Academic Publishers 66/3(2007-02-01), 373-390 0169-3913 66:3<373 2007 66 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer