Publication Date:
2016-07-15
Description:
Spontaneous counter-current imbibition into a finite porous medium is an important physical mechanism for many applications, included but not limited to irrigation, CO 2 storage and oil recovery. Symmetry considerations that are often valid in fractured porous media allow us to study the process in a one-dimensional domain. In 1D, the onset of imbibition can be captured by self-similar solutions and the imbibed volume scales with . At later times, the imbibition rate decreases and the finite size of the medium has to be taken into account. This requires numerical solutions. Here, we present a new approach to approximate the whole imbibition process semi-analytically. While the onset is captured by a semi-analytical solution. We also provide an a priori estimate of the time until which the imbibed volume scales with . This time is significantly longer than the time it takes until the imbibition front reaches the model boundary. The remainder of the imbibition process is obtained from a self-similarity solution. We test our approach against numerical solutions that employ parametrizations relevant for oil recovery and CO 2 sequestration. We show that this concept improves common first order approaches that heavily underestimate early-time behaviour and note that it can be readily included into dual porosity models. This article is protected by copyright. All rights reserved.
Print ISSN:
0043-1397
Electronic ISSN:
1944-7973
Topics:
Architecture, Civil Engineering, Surveying
,
Geography
