Pulp & Paper Chemical Engineering, Kraft Digesters & Recovery Boilers
Kraft White Liquor Active/Effective Alkali & Sulfidity Formula
Calculate North American Na2O-Basis Active Alkali AA (g/L), Effective Alkali EA (g/L), White-Liquor Sulfidity (%), and Digester Effective Alkali Charge (% on Oven-Dry Wood).
Na2S hydrolyzes into ONE OH- and ONE HS- ion—so Effective Alkali counts only HALF of Na2S!
Kraft (sulfate) wood-chip digesters delignify softwood and eucalyptus chips into strong cellulose pulp using White Liquor containing NaOH and Na2S, universally titrated by TAPPI standards in equivalent grams per liter of Sodium Oxide Na2O (MW = 62.0 g/mol)! In hot aqueous cooking liquor, sodium sulfide hydrolyzes completely via Na2S + H2O -> NaOH + NaHS: half of its sodium generates active hydroxide OH- while the other half forms hydrosulfide HS- (which selectively cleaves beta-aryl ether lignin bonds without peeling cellulose chains)! Therefore, Active Alkali is AA = NaOH_as_Na2O + Na2S_as_Na2O (g/L), Effective Alkali counts ONLY hydroxide equivalents EA = NaOH_as_Na2O + 0.5 * Na2S_as_Na2O (g/L), and White-Liquor Sulfidity is S_pct = (Na2S_as_Na2O / AA) * 100!
Verify on a Softwood Continuous Digester Liquor Lab Titration—NaOH_as_Na2O = 95.0 g/L (B2), Na2S_as_Na2O = 35.0 g/L (B3), and White_Liquor_to_Wood_Volume = 1.60 m³/t OD wood (Wait: let us check 1.60 vs 4.00! At 1.60 m³ white liquor/t OD wood, 112.5 * 1.60 / 10 = 18.00% EA on OD wood; at 4.00 m³ total liquor/t, let us use White_Liquor_Charge_m3_per_t_OD_Wood = 1.60 m³/t -> 112.5 * 1.60 / 10 = 18.00% realistic Kraft EA charge on wood!): Active Alkali AA hits 95 + 35 = 130.00 g/L Na2O (E2), Effective Alkali EA equals 95 + 17.5 = 112.50 g/L Na2O (E3), Sulfidity equals (35 / 130) * 100 = 26.92% (E4), and Digester EA Charge on Oven-Dry Wood ((EA * WL_m3_t) / 10) equals 18.00% Na2O on OD wood (E5)!
| Kraft White Liquor KPI (NaOH=95, Na2S=35 g/L as Na2O, 1.60 m³ WL/t Wood) | Formula | Verified Output |
|---|---|---|
| Active Alkali AA (g/L as Na2O) | NaOH_g_L + Na2S_g_L | 130.00 g/L |
| Effective Alkali EA (g/L as Na2O) | NaOH_g_L + 0.5 * Na2S_g_L | 112.50 g/L (107.50 @ 85/45 split) |
| White-Liquor Sulfidity (%) | (Na2S_g_L / Active_Alkali_AA) * 100 | 26.92% (34.62% @ 85/45 split) |
| EA Charge on OD Wood (% Na2O) | (Effective_Alkali_EA * WL_m3_t) / 10 | 18.00% (17.20% @ 85/45 split) |
TAPPI Na2O-Basis Kraft Sulfidity & Effective Alkali Formula
Validate NaOH_g_L > 0, Na2S_g_L >= 0, and White_Liquor_Volume_m3_t in (0.5, 5.0]!
=LET(oh_g, B2, s2_g, B3, wl_v, B4, IF(OR(oh_g <= 0, s2_g < 0, wl_v <= 0.5, wl_v > 5), "Invalid Liquor Titration", LET(aa_g, oh_g + s2_g, ROUND((s2_g / aa_g) * 100, 2))))High-Sulfidity Recovery-Boiler Reduction Shift Check (Set NaOH = 85, Na2S = 45 g/L)
Shift sulfur makeup at constant 130 g/L Active Alkali (B2 = 85.0 g/L NaOH, B3 = 45.0 g/L Na2S): Sulfidity E4 climbs from 26.92% to 34.62%, while Effective Alkali E3 dips from 112.50 to 107.50 g/L (lowering EA on Wood E5 from 18.00% to 17.20% unless white-liquor flow is trimmed upward)!
=IF(ISTEXT(E4), E4, ROUND(((B2 + 0.5 * B3) * B4) / 10, 2))Try the example
Use the original values or change them to test your understanding.