The following figure provides an overview of the non-conservative mass transport processes:

 

Non-conservative mass transport processes

 

When including the adsorption processes in the transport equation, it should be noted that the total mass of the substance under consideration in a reference volume does not only consist of the dissolved and transported substance quantity (nc), but also of the adsorbed substance quantity

(c_s(1 - n)ρ_s)

 

exists. The concentration of the adsorbed substance (c_s) is related to the solids content (1-n), whereby the density of the matrix (ρ_s) must also be taken into account.

In this case, the following term must be included in the transport equation:

 

With:

R₁ = proportion of non-conservative mass transport processes from adsorption

c_s = adsorbed concentration in the matrix [kg/kg]

n = flow-effective pore space [-]

ρ_s = density of the matrix [kg/m³]

 

The adsorption rate is described by a function c_s = f(c), which is optionally defined by the adsorption isotherm according to Henry, Freundlich or Langmuir.

When considering production or degradation, it must be taken into account that this theoretically occurs both in the fluid and in the matrix. The corresponding term R therefore consists of two parts with different degradation or production functions for the solution in the fluid f(c) and the adsorbed substances in the matrix f_s(c_s):

 

With:

R₂ = Proportion of the non-conservative mass transport process from production or degradation

 

When calculating mass transport in SPRING, however, production and degradation processes are only considered in the fluid, as it is not possible to separate these processes in nature.

Due to the irreversibility of these processes, no storage takes place here!

 

Instead of taking production and degradation into account, it is possible to have a half-life calculation carried out.

The corresponding term R₃ then results in:

R₃ = nS_rc(t)

 

With:

R₃ = Proportion of the non-conservative mass transport process from half-life

 

Boundary and initial conditions