Gypsum Crystallization During Phosphoric Acid Production: Modeling and Experiments Using the MSE Thermodynamic Model You Peng,†,‡ Zhilong Zhu,†,‡ Richard D. Braatz,† and Allan S. Myerson∗,† Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 E-mail: [email protected]

Supporting Information The model equation in terms of the first four moments are dµ0 dt dµ1 dt dµ2 dt dµ3 dt

µ0 τ µ1 = Gµ0 − τ µ2 = 2Gµ1 − τ µ3 = 3Gµ2 − τ = B0 −

(1) (2) (3) (4)

and the initial condition is Z

∞

Li fseed dL.

µi (0) =

(5)

0 ∗

To whom correspondence should be addressed Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 ‡ Co-first authors that equally contributed to this work †

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Table 1: Summary of literature solubility data used for estimating interaction parameters in the OLI MSE model Source Taperova, 1940 & 1945 1,2

Kurteva, 1961 3

System CaSO4 -P2 O5 -H2 O CaSO4 -P2 O5 -H2 O CaSO4 -P2 O5 -H2 O CaSO4 -P2 O5 H2 SO4 -H2 O CaSO4 -P2 O5 H2 SO4 -H2 O CaSO4 -P2 O5 H2 SO4 -H2 O

CaSO4 hydrate form Dihydrate Hemihydrate Anhydrite Dihydrate

Temperature range (℃) 25, 40, 60, 80 25, 40, 60, 80 25, 40 60, 80 25 50, 70

Hemihydrate

70

Anhydrite

70

Table 2: Fitted interaction parameters included in the MSE model Species i CaSO4 CaSO4 CaSO4 CaSO4 H3 PO4 Species i CaSO4 CaSO4 CaSO4 CaSO4 H3 PO4 H2 PO− 4

Species j H2 PO− 4 H3 PO4 P2 O5 H3 O+ P2 O5 Species j H2 PO− 4 H3 PO4 P2 O5 H3 O+ P2 O5 P2 O5

b0,ij -15849 -28.897 -5883.477 1037.96

b1,ij -0.831 -0.125828 -15.10225 -59.7945

b2,ij 5557015 929.758 -2868256 3514190

c0,ij 18566.29 17.875 11590.77 -4012.7

c1,ij 1.15 0.01288 15.19086 73.93

c2,ij -6466615 647.7436 2204956 -3626966

b3,ij b4,ij -0.00784 -30.1024 -0.000098 1.288 -0.0432 -0.008245 -22.0713 -0.000045 c3,ij c4,ij 0.0065 83.957 0.00034 3.0365 0.0343 0.00569 59.33 -0.0000069 -0.000295

Table 3: Specifications in the MSMPR simulation Description ∆t kv gypsum density relative error tolerance in ode15s relative error tolerance in OLI threshold for OLI computation CSD for seeded crystal

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Value 0.2 min 10 2.32×10−12 g/µm3 1 × 10−3 1 ×10−6 0.1% change in ∆µ3 Normal distribution (µ = 90 µm, σ = 8 µm)

References (1) Taperova, A. A. L’Analyse Physicochimique Dans Le Domaine Du Traitement Des Phosphates Par L’Acide Sulfurique. Zh. Prikl. Khim. 1940, 13, 634–651. (2) Taperova, A. A.; Shulgiva, M. H. Solubilities of CaSO4 Hydrates in Phosphoric Acid. Zh. Prikl. Khim. 1945, 18, 521–528. (3) Kurteva, O. I.; Brustkus, E. B. Solubilities of Calcium Sulfate In H3 PO4 + H2 SO4 and H3 PO4 + H2 SiF6 acid Mixtures. Zh. Prikl. Khim. 1961, 34, 1714–1722.

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