Concentrate to ammonium paratungstate through four CSTR-like stages: the process-flow and mass-balance view of the 3D plant.
Runs 60 simulated hours silently, then compares the measured APT rate and the W mass balance against the closed-form prediction.
The science
Scheelite is opened with soda in an autoclave: CaWO4 + Na2CO3 -> Na2WO4 + CaCO3 (wolframite uses NaOH). Impurities (Si, P, As, Mo) are precipitated, tungsten is concentrated on ion-exchange resin and eluted as ammonium tungstate, and APT (NH4)10[H2W12O42]·4H2O crystallizes on evaporation.
Each stage i holds tungsten mass w_i and obeys dw_i/dt = in_i - w_i/tau_i; a fraction R_i of the outflow goes on, the rest leaves in residues. Steady state: APT = F · g · (M_W/M_WO3) · R1R2R3R4 / x_W, where x_W is the tungsten mass fraction of APT (computed from atomic masses). Autoclave recovery: R1 = 0.985·(1 - e^(-5a)) with alkalinity a; seeding raises crystallization recovery from 0.92 to 0.95.
Honest limits: lumped first-order stages, constant recoveries and no temperature or reagent-cost model. The numbers illustrate the mass balance, they are not plant data.