Discussion Forum

Dear all,

I am trying to simulate an open thermochemical reactor for the hydration of MgCl2.2H2O to MgCl2.6H2O.
For this, a two step reaction is taking place :
MgCl2.2H2O + 2H2O --> MgCl2.4H2O (1)
MgCl2.4H2O + 4H2O --> MgCl2.6H2O (2)

The governing equations used for the model are :

The Water Mass Balance (Water Vapor Concentration)

∂C/∂t+u ∂C/∂x-D_x (∂^2 C)/(∂x^2 )+((1-ε_b ))/ε_b ρ_p ∂X/∂t=0

Energy Balance (Air Temperature Calculation)

(ρC_p ) ∂T/∂t+ε_b ρ_g C_(p,g) u ∂T/∂x-k_eff (∂^2 T)/(∂x^2 )-(1-ε_b ) ρ_p ∂X/∂t ΔΗ=0

Kinetics (Reaction Advancement)


Hydration:
∂X/∂t=k_cin (1-X)(1-(p_eq (T))/p_v )

Dehydration:
∂X/∂t=k_cin (X)(1-(p_eq (T))/p_v )


C: Water vapor concentration (mol/m3)
u: Air velocity (m/s)
Dx: Axial dispersion (m2/s)
εb: Bed porosity (-)
X: Advancement of the hydration (mol/kg)
Cp: Specific Heat Capacity (J/kg.K)
ΔH: Reaction Enthalpy (J/mol)
kcin:Kinectic constant (1/s)
peq: Equilibrium pressure (Pa)
pv: Vapor pressure (Pa)
ρp: Density of MgCl2.2H2O (kg/m3)
ρg: Density of saturated air (kg/m3)

I am using the Mathematics in Comsol to calculate those PDEs.
I added the PDE for hydration that describes the kinetics of the reaction (Added one X1 for the step from MgCl2.2H2O-->MgCl2.4H2O and another named X2 for MgCl2.4H2O-->MgCl2.6H2O)

The terms X1 and X2 ( advancement of reaction) take values from 0 to 1, so I added a condition for the second in order to start after X1 reaches almost 1.

During hydration, water is absorbed by the solid (MgCl2.2H2O), so the kinetics are affected (because Pv=C*R*T (Pa) ).
Could you please help me in order to find the "consumed" water (C) from X1 and X2, because, if there is not enough water concentration, then the second step should not be calculated.

Thank you so much for your time.

Many regards
Gerasimos