Mathematical and numerical filtration–advection–dispersion model of miscible grout propagation in saturated porous media

Abstract

SUMMARYThe development of a predictive model of behaviour of porous media during injection of miscible grout, taking into account convection, dilution and "ltration of grout solution with interstitial water, as well as consolidation aspects, is presented. Model assumptions are reviewed and discussed "rst. During the establishment of the model, we insist on surface terms and their physical relevance in expressing adsorption e!ects. Constitutive laws such as Fick's law for di!usive mass transport, hydrodynamic dispersion tensor dealing with miscibility, are modi"ed by taking into account "ltration e!ects. A new surface term appears in mass balance equations as a consequence of "ltration. According to the "ltration laws used, an initial "ltration rate is estimated on the basis of a one-dimensional experimental campaign. The "eld equations are discretized by using Galerkin "nite element and -scheme standard method. For transport equation, Streamline Upwind Petrov Galerkin method is employed to prevent numerical oscillations. Lastly, confrontation of numerical results with laboratory experiments constitutes a "rst step to validate the model on a realistic basis.

Real‐scale miscible grout injection experiment and performance of advection–dispersion–filtration model

“…The original model was developed by Bouchelaghem et al [1]. The theoretical study was justi"ed by the fact that most of the existing works relating to injection consist of experimental research activities, relying on particular grout and soil conditions or de"nite injection techniques, and do not tend to describe fundamental phenomena involved in grouting.…”

“…The second choice was retained because when employing the phenomenological approach for writing macroscopic balance equations, it is implicitly assumed that the macroscopic balance or constitutive equations of interest are of the same form as their microscopic counterparts. Using this approach, physical or chemical interactions between the di!erent phases composing the porous medium, essential for describing the adsorption process on microscopic interphase surfaces, are lost [6]. In the same way, miscibility between grout and interstitial water, which can be explained by invoking heterogeneities of real (microscopic) #uid velocity "eld and tortuosity of the path followed by a #uid particle within the interstitial void space [7], is properly described by considering the microscopic #uid component mass balance equation to derive the corresponding macroscopic equation.…”

A bio-chemo-hydro-mechanical model for microbially induced calcite precipitation in soils

“…In the most recent studies on advanced grouting fluid transport analysis [18][19][20][21], filtration is a key element in these mathematical formulations. Bouchelaghem and Vulliet [18] also consider a deformable soil, as well changing permeability, density and viscosity following the grout injection.…”

“…Bouchelaghem and Vulliet [18] also consider a deformable soil, as well changing permeability, density and viscosity following the grout injection.…”

“…When dealing with either strain in porous medium or the transport of extensive quantities in a deformable porous medium, we need to refer to the stress in the porous medium as a whole [41]. This stress is obtained by writing the global momentum balance with the Terzaghi effective stress principle [18].…”