PNG 550
Reactive Transport in the Subsurface

10.1. Introduction

PrintPrint

In this lesson we are not going to introduce new concepts. The flow and transport processes in homogeneous and heterogeneous systems (1D and 2D) have been introduced before. Similarly, mineral dissolution has also been discussed in a previous lesson. These processes are typically coupled in heterogeneous porous media, meaning they can affect each other. That is, flow influences reactions, and reactions can also have impacts on flow.

In a system where both physical flow and transport and reactions coexist, a general governing equation for any dimension system is as follows:

∂ ∂t ( ϕ C i )+∇⋅(−ϕD∇ C i +v C i )= r i,tot , i=1,2,..., N p MathType@MTEF@5@5@+=faaagCart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYlf9irVeeu0dXdh9vqqj=hHeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vqpi0dc9GqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamaalaaabaGaeyOaIylabaGaeyOaIyRaamiDaaaadaqadaqaaiabew9aMjaadoeadaWgaaWcbaGaamyAaaqabaaakiaawIcacaGLPaaacqGHRaWkcqGHhis0cqGHflY1caGGOaGaeyOeI0Iaeqy1dyMaaCiraiabgEGirlaadoeadaWgaaWcbaGaamyAaaqabaGccqGHRaWkcaWH2bGaam4qamaaBaaaleaacaWGPbaabeaakiaacMcacqGH9aqpcaWGYbWaaSbaaSqaaiaadMgacaGGSaGaamiDaiaad+gacaWG0baabeaakiaacYcacaqGGaGaaeiiaiaadMgacqGH9aqpcaaIXaGaaiilaiaaikdacaGGSaGaaiOlaiaac6cacaGGUaGaaiilaiaad6eadaWgaaWcbaGaamiCaaqabaaaaa@5EDA@
(1)
 

where Φ is porosity, Ci is the concentration of a primary aqueous species i (mol/m3), D is the hydrodynamic dispersion tensor (m2/s), u is the flow velocity (m/s), ri,tot is the summation of rates of multiple reactions that the species i is involved (mol/ m3/s) , and Np is the total number of primary species. Solving Np equations simultaneously gives the concentrations of primary species at different time and locations, which can then be used to solve for the concentrations of secondary species through laws of mass action (equilibrium relationship of fast reactions).

The equation (1) is general for systems with different number of dimensions (one, two, or three dimensions). Note that this is similar to the governing equation that we discuss in the 1D chemical weathering lesson, except that here we do not specify the dimension. If we specify this for 1D system, it will then be the same from as the governing equation in the 1D chemical weathering lesson.

Also note that in this equation, the dispersion coefficient and the velocities are written as tensors or matrix (in bold symbols) and can have different values in different locations. In fact, all porous medium properties, including porosity, permeability, and surface area can have spatial variations, as we will see in the example.