Pemodelan Matematis dan Simulasi Nanofiltrasi dalam Pemurnian Rejected Brine: Pengurangan Ion Ca, Mg, dan SO4 untuk Produksi Garam Kemurnian Tinggi

Sugianto, Mohamad (2026) Pemodelan Matematis dan Simulasi Nanofiltrasi dalam Pemurnian Rejected Brine: Pengurangan Ion Ca, Mg, dan SO4 untuk Produksi Garam Kemurnian Tinggi. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Rejected brine dari proses pemurnian garam umumnya masih mengandung ion penyebab kesadahan (Ca²⁺, Mg²⁺) serta ion divalen (SO₄²⁻) yang perlu dikurangi agar produk garam bernilai lebih tinggi. Penelitian ini menyusun pemodelan matematis dan simulasi nanofiltrasi (NF) pada modul spiral-wound untuk memprediksi kinerja hidrolika, transport ion multikomponen, serta proyeksi kemurnian garam berbasis komposisi permeat. Model dibangun menggunakan kerangka DSPM–DE yang dikopel dengan Extended Nernst–Planck (ENP) dan neraca massa sepanjang modul pada variasi tekanan umpan 2.5 - 12.5 bar dan debit umpan 1.20 - 3.60 m³/hr. Hasil uji kewajaran hidrolika menunjukkan fluks pelarut meningkat hampir linear terhadap tekanan, dari sekitar 1.753×10⁻⁶ hingga 1.335×10⁻⁵ m/s, dengan permeabilitas hidrolik efektif Lp ≈ 1.18×10⁻¹¹ m·Pa⁻¹·s⁻¹. Secara keseluruhan, laju permeat meningkat dengan tekanan dan menurun saat debit umpan dinaikkan, sehingga recovery satu lintasan berada pada kisaran ~4–31%. Target recovery minimum 15% digunakan sebagai acuan praktis pemilihan kondisi operasi yang masih relevan secara aplikasi, karena sesuai dengan kondisi uji standar pada material datasheet membran KeenSen (seri NF1) yang melaporkan kinerja rejeksi garam pada recovery 15%. Dekomposisi mekanisme menunjukkan konveksi dominan untuk semua ion, sedangkan difusi dan elektromigrasi lebih berperan pada ko-ion (terutama Cl⁻ dan SO₄²⁻). Pada kondisi operasi terpilih (Pf = 10 bar), urutan selektivitas mengikuti pola NF klasik: Na⁺ 71-75% < Cl⁻ 87-89% < Ca²⁺ 96,0-96,6% ≈ Mg²⁺ 97,7-98,1% < SO₄²⁻ 99,1-99,3%. Proyeksi stoikiometrik konservatif ke “dry-salt” dari permeat menghasilkan fraksi massa NaCl 96,98 wt%, dengan pengotor utama MgCl₂, Na₂SO₄, dan CaCl₂. Validasi terhadap rujukan literatur berbasis simulasi dan eksperimen menunjukkan kesesuaian yang baik terutama untuk ion divalen, sehingga model ini dapat digunakan sebagai dasar penentuan kondisi operasi NF sebagai unit pretreatment menuju produksi garam berkadar NaCl tinggi melalui skema kristalisasi lanjutan yang sesuai.
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Rejected brine from salt-refining operations typically still contains hardness-forming ions (Ca²⁺, Mg²⁺) and divalent ions (SO₄²⁻) that must be reduced to obtain higher-value salt products. This study develops a mathematical model and simulation of nanofiltration (NF) in a spiral-wound module to predict hydraulic performance, multicomponent ionic transport, and the projected salt purity based on permeate composition. The model is formulated using the Donnan–Steric Pore Model with Dielectric Exclusion (DSPM–DE) coupled with the Extended Nernst–Planck (ENP) framework and axial mass balances along the module, under feed pressures of 2.5 - 12.5 bar and feed flow rates of 1.20 - 3.60 m³/h. Hydraulic plausibility tests indicate that the solvent flux increases nearly linearly with pressure, from approximately 1.753×10⁻⁶ to 1.335×10⁻⁵ m/s, corresponding to an effective hydraulic permeability of L_p≈1.18×10^(-11)m·Pa⁻¹·s⁻¹. Overall, permeate production increases with pressure and decreases with increasing feed flow rate, yielding a single-pass recovery of ~4 - 31%. A minimum recovery target of 15% is adopted as a practical operating criterion because it aligns with the standard test condition reported in the KeenSen NF1 membrane datasheet, where salt rejection performance is specified at 15% recovery. Mechanistic decomposition shows that convection dominates transport for all ions, while diffusion and electromigration contribute more substantially for co-ions, particularly Cl⁻ and SO₄²⁻. At the selected operating point (Pf = 10 bar), the predicted rejection follows the typical NF selectivity hierarchy: Na⁺ 71 - 75% < Cl⁻ 87 - 89% < Ca²⁺ 96.0 - 96.6% ≈ Mg²⁺ 97.7 - 98.1% < SO₄²⁻ 99.1 - 99.3%. A conservative stoichiometric projection of the permeate into a “dry-salt” composition yields 96.98 wt% NaCl, with MgCl₂, Na₂SO₄, and CaCl₂ as the main impurities. Validation against both simulation-based and experimental literature indicates good agreement, particularly for divalent ions, supporting the use of the developed model as a basis for selecting NF operating conditions as a pretreatment step toward producing high-NaCl salt via appropriate downstream crystallization schemes.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	nanofiltrasi; DSPM-DE; Extended Nernst-Planck; rejected brine; selektivitas ion; spiral-wound; garam kemurnian tinggi. nanofiltration; DSPM-DE; Extended Nernst–Planck; rejected brine; ion selectivity; spiral-wound; high-purity salt.
Subjects:	Q Science > Q Science (General) > Q180.55.M38 Mathematical models
Divisions:	Faculty of Industrial Technology and Systems Engineering (INDSYS) > Chemical Engineering > 24101-(S2) Master Thesis
Depositing User:	Mohamad Sugianto
Date Deposited:	02 Feb 2026 10:41
Last Modified:	02 Feb 2026 10:41
URI:	http://repository.its.ac.id/id/eprint/131699

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