Solute transport including kinetic reaction

Overview

This scenario describes the transport of two solutes (Snythetica and Syntheticb) through a saturated media. Both solutes react to Productd according to \(\text{Productd}=\text{Synthetica}+0.5~\text{Syntheticb}\). The speed of the reaction is described with a first–order relationship \(\frac{dc}{dt}=U(\frac{c_{\text{Synthetica}}}{K_m+c_{\text{Syntheticb}}})\). 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 discretized 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, Synthetica and Syntheticb are present at simulation start–up at concentrations of \(c_{\text{Synthetica}}(t=0)=c_{\text{Syntheticb}}(t=0)= 0.5\) mol kg^-1_water, the influent concentration is 0.5 mol kg^-1_water as well. Productd 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-7 mol kg^-1_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 assignement of the boundary conditions. The horizontal domain is 0.5 m in x and 0.5 m in y direction, and, discretized into 10374 quadratic elemtents with an edge size of 0.0025 m.

Results

The kinetic reaction results in the expected decline of the concentration of Synthetica and Syntheticb, which is super-positioned by the influx of these two educts through the left side. By contrast, the concentration of Productd increases in the domain. Over time, opposed concentration fronts for educts and Productd 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 Productd 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.