Crystallizer simulation

1 feed -> solid crystals + mother liquor

Governing equations

The exact equations the solver works for a crystallizer — the same math shown in the app's "Theory" panel, not a black box.

$B$

nucleation rate — how many new crystals appear [#/m³/s]

$G$

linear growth rate [m/s]

$k_b, k_g$

nucleation and growth rate constants

$\Delta C$

supersaturation [mol/m³] — the driving force for both nucleation and growth

$C, C_{sat}$

actual and saturation concentrations [mol/m³]

$b, g$

nucleation and growth order

$m_0..m_3$

moments of the crystal size distribution (count, length, area, volume)

$\tau$

residence time [s]

$\bar L$

mean crystal size [m] = Gτ — the product-quality number

$\rho_c$

crystal density [kg/m³]

$k_v$

volume shape factor

$\dot m_{solid}$

crystal mass production [kg/s]

$\Delta H_{cryst}$

heat of crystallization [J/mol]

$Q$

duty [W]

Parameters

solute [feed component]; MSMPR: csat [mol/L], feed_concentration [mol/L], residence_time [s], optional kb/b/kg/g kinetics, crystal_density [kg/m^3], kv, molar_mass [kg/mol] — OR short-cut yield [0..1]; optional temperature [K], heat_of_crystallization

Example flowsheets that use it