Upscaling Flow and Transport Processes in Porous Media: from Pore to Core

UPSCALING FLOW AND TRANSPORT PROCESSES IN POROUS MEDIA: FROM PORE TO

CORE

R.C. Acharya (PhD student)

WUR, Department of Environmental Sciences

Sub-Department Soil Quality

The objective of this research is the identification and description of reactive solute transport at the pore scale, upscaling to the core scale and testing the upscale theories with the aid of laboratory experiments.

Introduction

During miscible displacemnet, reactive solutes in saturated soils are transported as a single fluid phase, water usually being the carrier. Among others, the most common transport case that one encounters is adsorption, which in large is controlled by the reactivity of the fluid phase and the chemical affinity and physical heterogeneity of the solid phase. Adsorption is in general described through linear or non-linear isotherms. Understanding of solute transport in porous media is built upon experimental and theoretical advances. Most commonly used theoretical tool is modeling. Modeling contaminant transport involves consideration of many complex interacting processes, including the physical flow field, and transport properties such as dispersivity, porosity, adsorption characteristics, microbiologically mediated degradation reactions and solid phase reactions. These processes are commonly simplified by the convection-diffusion equation (CDE) for homogeneous media. In practice, macroscopically homogeneous media are made of microscopically heterogeneous pores. Central to our approach is the hypothesis that the microscopic spatial heterogeneity of soil architecture influences the flow and activity of solutes within a soil column. A close insight of interactions of different types of isotherms and microscopic heterogeneity of porous medium can be gained through a hydraulic pore network model developed at Wageningen University (Figure 1). In HYdraulic POre Network model (HYPON), fundamental laws of physics are applied at the pore scale whereas the macroscopic quantities (such as permeability, dispersivity and concentration) are obtained through averaging.

In the present code of HYPON, we have included two types of porous media: microscopically homogeneous and microscopically heterogeneous with microscopically homogeneous chemistry (i.e. adsorption affinity does not vary spatially) and microscopically heterogeneous chemistry (i.e. adsorption affinity varies in space).

This research project started in January 2000 and it is due to finish in January 2004.

Results in 2002

The computer code for 3D-HYPON (written in C++) has been completed. The present code includes four modules: (1)-hydraulics, (2)-non-reactive tracer transport, which includes advection and mechanical dispersion, (3)-linearly reactive solute transport, which includes all processes included in (2) plus linear adsorption onto the solid phase and (4)- non-linearly reactive solute transport, which includes all processes included in (2) plus non-linear adsorption described by Freundlich isotherm.

Using the pore network model HYPON as the point of departure, solute transport has been incorporated, taking into account convection and numerical dispersion. The extended HYPON model was applied for homogeneous and heterogeneous (with regard to pore size) networks, to assess how macroscopic dispersion, i.e. the dispersivity, depends on pore size parameters and their spatial variation. It has been established that dispersivity depends according to a quadratic function on the variance of pore size and that this function differs for different mean pore sizes (i.e., a family of functions is obtained , Figure 2a). Comparing the breakthrough curves for pore networks with analytical solutions provided in literature, it appears that the network is large enough to be considered as representative: the agreement is fine and indicates that different transport in differently sized pores can be adequately described by a continuum CDE with a single dispersivity (for each realisation or for each ensemble of realisations that have one set of pore size statistics). Hence, to describe transport, only one realisation is needed as ergodicity is ascertained. An example of thus computed transport is displayed in Figure 2b.

a. / b.
Figure 1: Hydraulic POre Network: a. 3D-architecture of HYPON; b. Preferential paths of flow in HYPON (schematic display of fastest flow paths: from the top to the bottom.)
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Figure 2: Results of transport in HYPON: a. Dispersivity as a function of standard deviation of pore body sizes variance b. Concentration profiles in HYPON compared with travelling wave solution.

Research plan for 2003

It is aimed to broaden the set of simulations such that it becomes possible to understand and quantify dependencies between input and output of different cases, to firmly base conclusions on with regard to the development of travelling waves, and to scout similar situations for other chemical reactions such as chemical precipitation kinetics in the pore system. In 2003, also the different papers will be prepared and submitted, as well as the writing of dissertation will be continued.

Publications in 2002

Acharya, R.C., A. Leijnse, S.E.A.T.M. van der Zee; A comparative study of permeability: HYPON versus Carman-Kozeny Models. Proceedings Advances in Civil Engineering. Eds.: J.N. Bandyopadhyay and D.N. Kumar, New Delhi, 2002.

Acharya, R., A. Leijnse, and S.E.A.T.M. van der Zee, Construction of a hydraulic pore network model for consolidated and unconsolidated porous media: new method for discretization, in preparation, 2002

Supervised M.Sc. thesis

None.