Quantify the Pore Water Velocity Distribution by a Celerity Function

Wei Shao,Ye Su,Jakub Langhammer,Xieyao Ma,Zongji Yang

doi:10.1155/2018/1054730

Abstract

Celerity and velocity of subsurface flow in soil porous medium are intimately linked with tracer transport, while only few current studies focused on their relations. This study conducted theoretical analyses based on a pore bundle model, under which celerity in unsaturated flow is equivalent to maximum velocity. Furthermore, under 3 models Brooks-Corey model and unmodified and modified Mualem-van Genuchten models, we used a celerity function to derive breakthrough curves aiming to quantify the advective tracer transport for 5 typical soil textures. The results showed that the celerity under near-saturated conditions can be 5 up to 100 times larger than the saturated hydraulic conductivity, and a small volumetric fraction (<15%) of pores contributed more than half of the specific discharge. First arrival time and extensive tailing of the breakthrough curves were controlled by maximum velocity and velocity distribution, accordingly. As the kinematic ratio in the Brooks-Corey model remained constantly for each specific soil, we used it to quantify the ratio of maximum tracer velocity over average tracer velocity. We also found that a bimodal soil hydraulic function (for a dual-permeability model) may result in similar soil hydraulic conductivity functions for different parameter sets, but their celerities are different. The results showed that the proposed celerity function can assist in investigating subsurface flow and tracer transport, and the kinematic ratio could be used to predict the first arrival time of a conservative tracer.

Highlights

Subsurface flow is conducted in the soil porous medium, in which the pore structure controls the permeabilities and pore water velocities in numerous flow paths [1,2,3]
We extended the formulation to unsaturated soils and further formulated the tracer transport as a function of kinematic ratio αK that simplified (28) by replacingnBC: C t∗ ΔC
We conducted a theoretical study attempting to investigate the mechanism of pressure propagation and tracer transport in a subsurface flow system by analyzing the celerity in unsaturated flow

Summary

Introduction

Subsurface flow is conducted in the soil porous medium, in which the pore structure (i.e., pore connectivity, tortuosity, and pore size distribution) controls the permeabilities and pore water velocities in numerous flow paths [1,2,3]. It is impractical to deterministically represent the pore-scale fluid dynamics and transport processes in soil, for the variability of pore water velocity is difficult to observe or predict [4,5,6]. The soil hydraulic properties (e.g., the lumped hydraulic conductivity and moisture capacity) and state variables (e.g., volumetric water content and capillary pressure) are often quantified in a representative elementary volume (REV) [7, 8]. The continuum subsurface flow equation (i.e., the well-known Darcy-Richards equation) calculates specific discharge and average pore water velocity for transport phenomenon. The specific discharge quantifies the volumetric flow [9, 10], and the average pore water velocity can be coupled with an advection-

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