Phosphoric acid reactor-filter simulation

phosphate rock + sulfuric acid + wash water -> product acid, gypsum cake, off-gas; wet-process DH / HH / HDH attack, flash cooler and countercurrent cake wash

Governing equations

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

$n$

hydrate water (2 gypsum, 0.5 bassanite) [-]

$a_w$

water activity of the attack acid [-]

$a_w^{*}$

gypsum/bassanite transition water activity [-]

$\log K_{G}$

gypsum dissolution log K (LLNL) [-]

$\log K_{B}$

bassanite dissolution log K (LLNL) [-]

$f$

fraction of soluble P2O5 left in the washed cake [-]

$R$

wash ratio [-]

$N$

countercurrent wash stages [-]

$\eta_{P_2O_5}$

P2O5 recovery to the product acid [-]

$X$

attack efficiency [-]

$c$

co-crystallized P2O5 fraction [-]

$\dot n_{P,sol}$

soluble P lost with the cake liquor [mol/s]

$\dot n_{ap}$

fluorapatite fed [mol/s]

$\dot n_{evap}$

water evaporated in the flash cooler [mol/s]

$\lambda$

latent heat of water [J/mol]

$Q_{fc}$

flash-cooler duty [W]

$\mu$

filtrate viscosity [Pa s]

$\alpha$

specific cake resistance [m/kg]

$c_s$

dry cake per volume of formation filtrate [kg/m3]

$\Delta P$

filter vacuum [Pa]

$R_m$

filter medium resistance [1/m]

$v$

filtrate per filter area per cycle [m3/m2]

$t_f$

cake formation time [s]

$t_{cyc}$

filter cycle time [s]

$A$

filter area [m2]

$\dot m_s$

dry cake to the filter [kg/s]

$r_{P_2O_5}$

filtration rate [kg P2O5/(m2 s)]

$\dot m_{P_2O_5}$

P2O5 in the product acid [kg/s]

Parameters

wet-process phosphoric acid reactor-filter: the attack tank, the flash cooler and the gypsum filter in one block. Inlets: phosphate rock (fluorapatite, calcite, silica pseudo-components; port rock), sulfuric acid (port acid) and wash water or weak recycle acid (port wash). Outlets product_acid, gypsum_cake (solid), off_gas. route [DH|HH|HDH] (dihydrate, hemihydrate, hemi-dihydrate); temperature [K] (required; attack temperature); attack_efficiency [0-1] (required); cocrystallized_p2o5_fraction [0-1] (required; P2O5 lost in the sulfate lattice); fluorine_to_gas [0-1] and fluorine_to_cake [0-1] (required; the rest stays dissolved); cake_liquor_ratio [kg liquor/kg dry cake] (required); wash_stages [int] (required, countercurrent); calcite_conversion [0-1] (default 1.0); sulfate_excess [-] (target excess over the stoichiometric acid, checked and warned); h2so4_dilution_enthalpy [J/mol H2SO4] (optional override; computed from NBS 1982 heats of solution at each stream's strength when absent); attack_residence_time_s [s] and slurry_density_kg_m3 [kg/m3] (optional attack-tank sizing, none defaulted); recrystallization_temperature [K] and recrystallization_p2o5_wt [0-1] (HDH); pressure [Pa]. Optional gypsum filter sizing (Ruth constant-pressure filtration; given any filter_* key, all of these are needed and none is defaulted): filter_specific_resistance [m/kg] (cake alpha, measured), filter_medium_resistance [1/m], filter_vacuum_pa [Pa], filter_cycle_s [s], filter_form_fraction, filter_wash_fraction and filter_dry_fraction [0-1] (sector shares of the cycle), filter_filtrate_density_kg_m3 [kg/m3]; optional filter_type [tilting_pan|rotary_table|belt], filter_filtrate_viscosity_pa_s [Pa*s] (else the H3PO4/water fit to NIST data), filter_wash_viscosity_pa_s [Pa*s], filter_wash_density_kg_m3 [kg/m3], filter_cake_porosity [0-1] and filter_solid_density_kg_m3 [kg/m3] (cake thickness). Hydrate stability from LLNL log K(T) and the H3PO4/water activity; DH/HH windows warned

Example flowsheets that use it