Solute transport including kinetic reaction

• Parabolic/ComponentTransport/ReactiveTransport/KineticReactant_AllAsComponents/KineticReactant2.prj

Overview

This scenario describes the transport of two solutes (Synthetica and Syntheticb) through a saturated media. Both solutes react to Productd according to $\text{Product d}=\text{Synthetic a}+0.5~\text{Synthetic b}$. The speed of the reaction is described with a first–order relationship $\frac{dc}{dt}=U(\frac{c_{\text{Synthetic a}}}{K_m+c_{\text{Synthetic b}}})$. The coupling of OGS-6 and IPhreeqc used for simulation requires to simulate the transport of $H^+$–ions, additionally. This is required to adjust the compulsory charge balance computation executed by Phreeqc. The solution by OGS-6–IPhreeqc will be compared to the solution by a coupling of OGS-5–IPhreeqc.

Problem Description

1d scenario: The 1d–model domain is 0.5 m long and discretised into 200 line elements. The domain is saturated at start–up ($p(t=0)=$ 1.0e-5 Pa). A constant pressure is defined at the left side boundary ($g_{D,\text{upstream}}^p$) and a Neumann BC for the water mass out-flux at the right side ($g_{N,\text{downstream}}^p$). Both solutes, Synthetic a and Synthetic b are present at simulation start–up at concentrations of $c_{\text{Synthetic a}}(t=0)=c_{\text{Synthetic b}}(t=0)= 0.5~\textrm{mol kg}^{-1}~\textrm{water}$, the influent concentration is $0.5~\textrm{mol kg}^{-1}~\textrm{water}$ as well. Product d is not present at start–up ($c_{\text{Productd}}(t=0)=0$); neither in the influent. The initial concentration of $\text{H}^+$–ions is $1.0e\textrm{-}7~\textrm{mol kg}^{-1}~\textrm{water}$; the concentration at the influent point is the same. Respective material properties, initial and boundary conditions are listed in the tables below.

2d scenario: The 2d–scenario only differs in the domain geometry and assignment of the boundary conditions. The horizontal domain is 0.5 m in x and 0.5 m in y direction, and, discretised into 10374 quadratic elemtents with an edge size of 0.0025 m.

Table: Media, material and component properties

Table: Initial and boundary conditions

Results

The kinetic reaction results in the expected decline of the concentration of Synthetic a and Synthetic b, which is super-positioned by the influx of these two educts through the left side. By contrast, the concentration of Product d increases in the domain. Over time, opposed concentration fronts for educts and Product d evolve. Both, OGS-6 and OGS-5 simulations yield the same results in the 1d as well as 2d scenario. For instance, the difference between the OGS-6 and the OGS-5 computation for the concentration of Product d expressed as root mean squared error is 1.76e-7 mol kg$^{-1}$ water (over all time steps and mesh nodes, 1d scenario); the corresponding median absolute error is 1.0e-7 mol kg$^{-1}$ water. This verifies the implementation of OGS-6–IPhreeqc.