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.

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Parameter	Description	Value	Unit
$\phi$	Porosity	1.0
$\kappa$	Permeability	1.157e-12	$\textrm{m}^2$
$S$	Storage	0.0
$a_L$	long. Dispersion length	0.0	m
$a_T$	transv. Dispersion length	0.0	m
$\rho_w$	Fluid density	1.0e+3	$\textrm{kg m}^{-3}$
$\mu_w$	Fluid viscosity	1.0e-3	Pa s
$D_{\text{H}^+}$	Diffusion coef. for $\text{H}^+$	1.0e-7	m$^2$ s
$D_{solutes}$	Diffusion coef. for Synthetica, Syntheticb and Productd	1.0e-12	m$^2$ s
$U$	Reaction speed constant	1.0e-3	h$^{-1}$
$K_m$	Half–saturation constant	10	mol kg$^{-1}$ water

Table: Media, material and component properties

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Parameter	Description	Value	Unit
$p(t=0)$	Initial pressure	1.0e+5	Pa
$g_{N,downstream}^p$	Water outflow mass flux	-1.685e-02	mol kg$^{-1}$ water
$g_{D,upstream}^p$	Pressure at inlet	1.0e+5	Pa
$c_{Synthetica}(t=0)$	Initial concentration of Synthetica	0.5	mol kg$^{-1}$ water
$c_{Syntheticb}(t=0)$	Initial concentration of Syntheticb	0.5	mol kg$^{-1}$ water
$c_{Productd}(t=0)$	Initial concentration of Productd	0	mol kg${^-1}$ water
$c_{\text{H}^+}(t=0)$	Initial concentration of $\text{H}^+$	1.0e-7	mol kg$^{-1}$ water
$g_{D,upstream}^{Synthetica_c}$	Concentration of Synthetica	0.5	mol kg$^{-1}$ water
$g_{D,upstream}^{Syntheticb_c}$	Concentration of Syntheticb	0.5	mol kg$^{-1}$ water
$g_{D,upstream}^{Productd}$	Concentration of Productd	0.0	mol kg$^{-1}$ water
$g_{D,upstream}^{\text{H}^+}$	Concentration of $\text{H}^+$	1.0e-7	mol kg$^{-1}$ water

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.